LVLS in CoD4 how long do they take

Leveling up is purely based on kills and the chance of being on a winning team. They take longer the higher level you are, but you open up more challenges to get bonuses to level up quicker. Weapon upgrades are ranked solely on kills you get with that weapon, so that will be strictly up to you.

I'm level 14-15 and I've only played about 3 hours total, and have about 350 kills total. I mostly play Team Deathmatch.

your guns level from 25, 75, and 150 kills for the Assault, SMG, and LMG. SHotties are 25 and 50. and Snipers are 100.

As you gradually move your way up in levels, each new level will require higher XP to reach next rank respectively.

For example to reach level 5 from level 4 it could require 400 XP, however where I'm now from level 34 to reach 35 it will require 2400 XP

So, the higher you go, the more XP is needed. Its not really hard to be honest, play around with majority of the guns and get rewards XP while using them, this also goes for challenges. Many are not hard to do and will net good XP+ what you earn while you play.

Just have fun, and don't worry about levels. To unlock specific guns upgrades and accessories, you need to have a certain level as well as keep using the same gun for some time.

If you look at barracks, it will tell you the requirements.

All about how many points you accumulate. You can just go TDM and each kill is 10 points, 2 points for assists. You get bonus points for winning, points for completing challenges

Or try other game modes when you can. "Headquarters" can give you a lot of points, if your on the winning side, but it will hardly give you any if your team doesn't perform well.