JoeViking245

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.
 

The script you show is in the Running Script section of the emulator. (An educated guess)
To exit from the Pause Menu, that portion of the script [also] goes in the Exit Script section - 'The script to use when exiting from the Pause Menu'.
So in the emulators Exit Script section, put:
$Esc:: { if WinExist("JoyToKey") Process, Close, joytokey.exe Run, "D:\HFSBox\Utilities\JoyToKey\JoyToKey.exe" "Layout 8 Boutons.cfg" WinClose, ahk_exe {{{StartupEXE}}} } (while keeping the full script in the Running Script section.)
 
Note: I moved the 'close the emulator' to the last line.  I'm kind of surprise that when exiting from NOT in the pause menu that the script changes the profile back.
I say this because when the game is exited, the Running Script is essentially discarded/thrown-away/process-killed.  No matter where it's at.  It may be that the processes you have, take place "super-fast".  i.e. before the game is 'completely exited'.  That said, if it ain't broke, don't fix it.  

If you have autosave enabled in MAME itself (autosave 1), you don't need the -autosave parameter.  Adding that parameter just overrides whatever you have set in MAME.  Just like as if you executed MAME form the Windows command prompt.  
Same thing with "state_directory   sta" and the -state_directory <path> parameter.
 
If in LaunchBox you have Upload Your MAME High Scores... enabled (Tools < Options < Integrations < MAME), there's a caveat...
I know high scores and autosaves are 2 separate things.   But if it affects that, it's possible it has an effect on auto saves as well.  (I don't know for certain)

Edit you MAME emulator in LaunchBox and check the Command-line Parameters for -rompath %romlocation%.  If it is there, since you edited you own 'rompath' in mame.ini, remove that parameter and value.

When importing, the importer ignores everything inside parenthesis.  So probably the easiest way to keep your special numbers in the filenames would be to use a bulk file-rename utility and have it add parentheses around the number and then import those files with the 'new' filename. 
The 'new' filename would be for example:  (04.) Sonic The Hedgehog.ext

That's a good sign.  Try adding a 3 second timer before Process, Wait...  Giving the com commands a few moments to settle in.
If it still doesn't work, move the 1st 2 com commands into their own script and add that as an Additional App for the games and set them to Run Before Main App.  Try it on one or two and if it works, there's a plugin where you can bulk add Additional Apps to all the games [that need it].

Remove -fullscreen from the emulators Default Command-line Parameters (1st screenshot).  (It's not an available parameter [anymore?].)
Then, open [just] the emulator.  Go to Video - Display Configuration - and check Emulate Fullscreen and Fullscreen on ROM Open.

You have an extra - (dash) right before the "path\to\ROM.zip".  Remove it.
Run, %MAMERun% -"D:\LaunchBox Arcade\Games\Arcade\chasehq.zip", , Hide
Run, %MAMERun% "D:\LaunchBox Arcade\Games\Arcade\chasehq.zip", , Hide ; OR Run, %MAMERun% "%GameRDP%", , Hide  

Close LaunchBox.  (Click on it and press Alt+F4) Open Windows Explorer and navigate to //LaunchBox/Data/ Open Settings.xml with any text editor Find the line starting with <ControlsBarHeight> Set the value to 50 (is probably something like 1550, or some big number) <ControlsBarHeight>50</ControlsBarHeight>  
DO NOT TOUCH OR CHANGE ANYTHING OTHER THAN THAT NUMBER Save and close the file Restart LaunchBox Don't do what you did before to get it like that.