welcome to RCU
You are making a better start than most! Good purchases thus far.

And you pretty much have things right. You can charge at 1c, meaning 4amps for your 4000mah lipos. If you balance charge them, this will take alittle under 1 hour usually.
Fast charging means it will not balance the cells. Doing so takes extra time. While its not nessesary to balance charge most packs every time, it wont hurt them if you choose do. I personally always balance charge mine.

KV means revolutions per volt. So a 2000kv motor on 7.4v should turn about 14,800 rpms (this rating is with no load on the motor of course.)

Larger and heavier models usually use a lower KV motor, as lower KV equates to more torque. To get the top speed, more voltage is added (in your case 14.8 or 4s)

The thunder you bought is reported to be a tough truck.
many RCU'ers use the imex b6, Ive had one and they are awsome for the money. And yes, it cannot charge above 5amps, so a 6cell lipo it can not charge at a full 1c.
That charger will beep loudly when charging is done and stop on its own.
Lipos can hold a full charge for a good long time. there is no need to keep them on the charger in storage mode. I dont leave mine fully drained for more than a week. But when fully charged I may not use them for a couple of weeks.

If you do not yet have a lipo sack, its a good idea to get one. Tho lipo issues are very rare, a lipo CAN (threw a faulty charger or user error) burst into flames. A lipo sack is a fire "resistant" sack that you put the lipo into when chargering. It can give you time to throw the lipo out of the house before it catches anything else on fire. Again, its VERY RARE, but always best to spend the $12 on the extra protection than to risk it.