JoeViking245

Correct.  BigBox is not setup to manage your games.  Just looks pretty and plays games.

Looks like I missed saying to uncheck the "Remove quotes" and also the "Remove file extension..." boxes.  Srry 'bout that.

In FinalBurn Neo: Misc < Configure ROM paths...    Set the path to your ROM folder(s) [if not already]. In LB, edit the emulator and check the boxes Remove Quotes and Remove file extension and folder path. At least that's what worked for me. I got the same error with those 2 un-checked.
 

Un-check Remove Quotes.
Also, add --nogui to the Default Command-Line Parameters.

MAME is for Arcade games.  Appears you had imported them into the Windows platform (vs the typical Arcade platform).
By default, LaunchBox sets the metadata/media scraping for Windows platform to Windows [PC Games].
If you wish to keep your Arcade games in the "Windows" platform, edit the platform and set the Scrape-As value to "Arcade" and re-scrape the metadata/media.
A more prudent approach could/would/should be to remove all the MAME (Arcade) games from the Windows platform and then [re]import your MAME ROMs into the Platform "Arcade".  Then when you download images, you'll get the ones for Arcade games and not PC Games.

I'm fairly certain your "mame64.exe" is from an older version of MAME.  Being older is not the issue (and nothing to be concerned with). 
However, having the command-line parameter -keyboardprovider dinput would be an issue with older versions.
Edit your MAME64 emulator ('Edit/Bewerken' from screenshot above) and try removing that and see if it [now] works. 

If it's showing when LaunchBox is first being started (aka when 1st launched/loaded), I'd say LaunchBox is [still] attempting to load an eXo ('exodos stuff') remnant.
Assuming you're starting it via LaunchBox.exe (vs. a batch file or script), look in Tools < Options < Startup Applications and see if there's anything eXo related.  If there's nothing in there, I'd next look in the /LaunchBox/Plugins/ folder.  Not sure exactly what would be 'eXo' there.  But those 2 locations should/would be the only places LB would start something extracurricular (aside from a batch file or a script that starts LB).

If, when you disable G-Drive syncing and you're happy with how LaunchBox/BigBox performs via G-Drive (which I guess at this point is actually running from your local G-Drive folder), then...
 
A variation of a Google search result looks like this:
This link mentions "googledrivesync.exe" which is now "GoogleDriveFS.exe" (at least on my PC). It seems there's no command-line parameters you can pass to the executable to turn G-Drive syncing on/off.  So you have to "kill" the process. From the Windows Command Prompt, to kill G-Drive altogether, you can run taskkill /IM GoogleDriveFS.exe /F Then to restart it, double click "GoogleDriveFS.exe".  Mine's located in "C:\Program Files\Google\Drive File Stream\100.0.2.0\"
 
LaunchBox/BigBox has a Startup Applications feature that can load an application when one or the other or both (or neither?) are started. (Which could be a batch file containing the above command.)
But there are no (immediately accessible) means to launch an app when either close.  "Immediately accessible" meaning, you could create a plugin that captures the System Event LaunchBoxShutdownBeginning and/or BigBoxShutdownBeginning and then (re)start the process "GoogleDriveFS.exe".
 
Alternately, you could create/use a batch file that handles the whole kit-and-caboodle.  Something like this (edit accordingly)
taskkill /F /IM GoogleDriveFS.exe timeout 5 start /w "" "D:\LaunchBox\Core\LaunchBox.exe" start "" "C:\Program Files\Google\Drive File Stream\100.0.2.0\GoogleDriveFS.exe" Do This:
Verify YOUR Google Drive executable is indeed "GoogleDriveFS.exe" Change the path to YOUR LaunchBox location DO point to the /LaunchBox/Core subfolder Change LaunchBox.exe to BigBox.exe if that is your preference Verify that is the path to YOUR "GoogleDriveFS.exe" If all's good/tested/working, make for a 'prettier' presentation...
Create a shortcut to the batch file Right-click the shortcut and select Properties Change Run from Normal Window to Minimized Click OK to save and close. Use the shortcut to start the "whole kit-and-caboodle".  The above makes it so the Command Prompt window does not appear.

The only times I've seen this happen is when I launch the game, and it's the 1st time Steam has been launched (on that particular day), and Steam has an update.  Steam will do its update thing and then show the "On Sale" and 'Main' windows.  This happens in the background, so you don't see anything when the game [eventually] starts, and you play it.  It's when you exit the game you see those windows still lurking [on top of BigBox].
I've gotten in the habit of, before I start BigBox, if I know I'm going to be playing a Steam game, I'll
Start Steam 1st.  Let it do its thing close/minimize Steam when it's done then start BigBox.

For this, you'd need to create a plugin (written on C#).
Essentially, it'd catch a selection change event, determine that the change went into a playlist (vs say a different game, a platform or a platform category) and that the playlist is 'your special playlist'.  From there, execute what you wanted done.
 

In your Flycast emulator folder, edit emu.cfg and set fullscreen to yes. 
[window] fullscreen = yes  
In LaunchBox, edit your Flycast emulator. In the Running Script put:
$Esc:: { WinClose, ahk_exe {{{StartupEXE}}} }  

I presume those folder names look similar to Platform names.  (That, or exactly like platform names.)  They're auto created when you have auto import enabled.  (For games. Not to confused with the auto import for storefronts.)   This allows you the proper folder names to drop your ROMs into to have LaunchBox import them from.

The keyboard shortcuts listed in that link are for their "LaunchBox" (referred to as "the LaunchBox").  Not to be confused with (this) Unbroken Software's LaunchBox.
You can Tab through the panes and then arrow Up/Down in the respective panes. Still, it's pretty 'clunky' that way as [the Real LaunchBox] it's meant to be a Windows based keyboard and mouse application.

View < Show/Hide - Text on All Games (or Ctrl+Shift+T).  But it won't show the File Names.  Just the Game Title.  

The games File Name can only be seen in the Game Details [right] panel.  To enable showing those, go to Tools < Options < Visuals < Game Details and check the box for File.

Yes and no. Those are 2 different licenses.  But there is [limited] free use of the Android app.
Download LaunchBox for Android
Free for 100 Games or Less
LaunchBox for Android is now free if you need less than 100 games. For an unlimited number of games, you can easily purchase a DRM-free license. But you might as well download and try out the app for free, first! It's super easy to install the license after purchasing, and it does not require a reinstall.

When in the Arcade platform, press Ctrl+N.  Type in the games Title.  In the Launching section, Browse to where the ROM is located and select it.  Click OK to save.
If it doesn't appear in with your other games, make sure you don't have 'Hide games missing media' (worded something like that) checked.  It'll be in the View menu.

In short. No.

To set the default images used for your platform, in LaunchBox:
Got to Tools < Manage < Platforms Select your platform  Click Edit (the easy way) From Windows File Explorer,  Select your image(s) drag and drop them onto the area below where it says Images Use the left and right arrows ('carrots') to switch images Click on the image type to change,,, well,, the image type. Once you've set them, click OK to save and close.

No.  LaunchBox calls AutoHotkey.exe directly from its /ThirdParty/AutoHotkey/ folder.  So you're safe to (re)associate your .ahk file extension to your personal installation of AutoHotkey.
 
Side note: you don't have to have it "installed" to be able to use it. 
i.e. You can launch your script directly like so...
"D:\LaunchBox\ThirdParty\AutoHotkey\AutoHotkey.exe" "D:\MyScripts\My Special Script.ahk"  

Edit the game Click Additional Apps Select the one you want as the default play-when-you-double-click-it [in the lower-right] click Make Default Now, if you want to change the Names (titles), you can.  But that won't affect which is the default game to launch.

The 3D Box Model and the 3D Box Image are 2 separate things.  One can never directly replace the other.
The 3D Box Image is not one of the image types that will display in the game Details (right) panel.  Regardless of disabling the 3D Box Model.
In LaunchBox, the only places to visually see the 3D Box Image are:
When you edit the game When you double-click one the of smaller images in the games Details panel (to make it show full screen) press the left or right arrow on the keyboard until you see that image Select Image Group and change it to 3D Boxes This will change the main (middle) section images to 3D Boxes (Image)

When you say "category", I'm hoping you mean "Platform" because that'd make it a lot easier.
 
To move them to a different Platform:
When in the Super Nintendo Entertainment System Platform, Select the games that you want moved and then press Ctrl+E to start the Bulk Edit Wizard.  For the Field, select from the dropdown, Platform.  For the Value, select (or you can manually type it in) Nintendo Super Famicom (or however you want to word and spell it).  Follow through the prompts to complete the process.

K.  Then have it not check for updates for that emulator.
Tools < Manage < Emulators  - Click on your emulator then right-click on the Status column (for that emulator) and select Don't check for updates.

That error message is from FinalBurn Neo. Not LaunchBox.
The emulator needs to know where your ROMs are located.  I encountered an issue when I set the path(s) [in the emulator] then closed it, they weren't being saved.  So be sure to click Save settings (step 4). 
Open FinalBurn Neo Go to Misc < Configure ROM Paths... Add the path(s) to where your ROMs are located Let it finish scanning Go to Misc Click Save settings to .ini now Close the emulator  
In LaunchBox, edit your FinalBurn Neo emulator Check the box Remove file extension and folder path UN-CHECK the boxes Remove Quotes (quotes are needed if using ROMS that have spaces in the filename) Extract ROM archives before running Click OK to save and close  
Play games

Looking at the Change Log, the multiple instances of LaunchBox/BigBox had some 'safety checks' added in version 5.3.