Okay I'm an experienced MTA player and I'll Answer these
1. Yes you can install mods (map, cars, handlings)
2. NO
3. No you can't save, their all a play and leave server
4. No you don't need a mod to enter stunt, you can go into either stunt or deathmatch depends on if you liek killing or stunting
5. Yes there are mods not cheats (the ones you type)
6. The only people and cars you see are the ones you play online with (meaning other actual online players)
7. No missions really, unless your in clan wars, or the admin is playing a game (cops and robbers) or your just setting a goal for your score
8. Usually there are 5-6 differ players to choose from, each of them have 2-3 unique skins that appear randomly if you choose em
EX: I choose Candy 5 times over the course of the game if i die
I might come out to be Candy 3 times, A Girl In white Thongs and a Cowboy Hat, and some Barbie Girl.
You just gotta play around with it until you get the hang of it
Hope I gave you all the info you need