1. Is there a way to keep the default scrolling games in the main menu since it has been removed? In /themes/cool_res/games_icon/ I can see only BattleCity pictures. I guess you deleted all others. Can I get them somehow back? Eventually from default SD card that came with the console?
Yes. In the tutorial I mention replacing some config with a transparent image: Simply copy the original config (ipen_en folder I think? Not sure this is from memory) from your original SD card instead to get the games back in the UI. You will then need to copy the game files themselves from the Fat32 partition of the original SD card to the Fat32 partition of your 16GB card, and it should just work.
2. Where do I put apps folder (@BVP provided calc, countdown, dgclock, dingus-write and startwatch + I want to download and try others)? Do I put those apps in 3.6 GB Fat32 partition or 105 MB Drive under /apps?
Technically either works as long as there is space for the app to be copied to the partition (really just an issue with the 105MB partition due to it's limited size). Just modify the UI config accordingly if you want the menus and things to see them, but you can also navigate to either place from the File Explorer to start any app you want (and as long as the app executable ends with the .dge extension).
3. Is there an emulator (Linux or Windows) to test all these before putting the SD Card back in the Console?
Not to my knowledge. It might technically be possible to re-create the (arm-based?) HW using virtual machine software, but I have no idea how to do that. I just tested changes and experimented on the real device, removing the card, modifying, and replacing again over and over (and over and over and over) again until it was what I wanted.