The custom classes can be changed normally in the lobby, but have a different setup than mw3.
You get 10 items basically ( guns, attachments, perks, grenades, tactical, all count towards that 10 ) to make a class, you can change your class anyway you want, its not like the tokens, but can only have a maximum of 10 items.
There are some other things that give you some things like, 3 attachments on your primary, extra perk slot, two lethal grenades, etc; I'll call them [ bonus ] for this explination ( I don't remember them all, but using these count as 1 item )
For example, I'll have a sniper ( 1 ) with extended mags ( 2 ), rocket launcher ( 3 ), 3 perks ( 6 ), semtex ( 7 ), emp grenade ( 8 ), [bonus-take two lethal grenades] ) 9 ), second semtex grenade ( 10 ).
I believe you get weapon experience the same way as in mw3, except in black ops 2, the higher your weapon level, the more attachments you unlock instead of like 'range' or 'kick' in mw3.
Any kills, captures( tactical gameplay like capture the flag, or hardpoint etc ), assists go towards your killstreaks. ( I don't believe your killstreaks stack, but if you use them you can get another one. )
For example, If I use Warthog, attack dogs, and vtol warship. ( After I get my highest killstreak, which would be the vtol, my killstreak xp will reset, and if I get more xp, ill get another warthog ( only if I used my previous one to make room for the next )
^ I'm not 100% sure on the killstreaks as I haven't played in a while.
I don't know about prestiging.
The unlock tokens you get, you might as well use asap. You get a ton of them, so there's no reason to save them.
As for the zombies, you would have to be more specific.