Main functions failure (USB Storage, WIFI, SIM, Camera) after boot in Samsung Galaxy Mini 2 running Android 2.3.6
200 apps on Gingerbread :O, time to upgrade now. Even on my OnePlus One with 3gigs RAM and 64gigs Internal Storage, I merely have 20-30 downloaded apps with 2-3 in start-up.

But anyhow, follow this:


Format and install some custom ROM like Cyanogenmod
Keep only required apps.
Remove apps from start-up. Use AIO Toolbox from Play Store.
Use AIO Toolbox on regular basis to clean up.


For all your apps backup: I believe in that list of 200 apps, you must have some system tools. Check if it has backup option for apps or not. Even you can create backup from recovery mode too, if your recovery supports. TWRP/Cyanogenmod/ClockWorkMod do have this option.