Yes, you must meet the level requirements for fighter bonus feats.
Fighters get to take more feats than other classes. Everyone gets a feat at 1st level and every 3rd level (so 1, 3, 6, 9, 12, 15, and 18), but fighters also get additional feats at 1st level and every even level (so 1, 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20).
In both cases, you need to meet all requirements for the feat you pick. Fighters don’t let you take feats more easily or anything, they just let you take more feats.
Now, Weapon Specialization et al. specifically require Fighter levels as part of their requirements. Whether you take them as a fighter bonus feat or as a regular feat, you can only take them if you have that many fighter levels. These are the only feats that are unique to fighters; every other feat a fighter can take, someone else could also take.
Anyway, long story short, as a Fighter 3, you could not take all of these feats. In fact, you could not take any of them, because they all require 4 or more levels of Fighter.
Now, that said, you should know that these are very weak feats. Weapon Focus is commonly used as a “tax” to get into prestige classes, and can be valuable for that (but not for itself), but the rest rarely are, and are therefore basically worthless. I strongly recommend that you do not take them. The only exception is Weapon Supremacy, which requires all the other Weapon Focus type feats from both the Player’s Handbook and Player’s Handbook II, plus Fighter level 18th. That feat is very good. It also comes way too late and requires way too many poor feats.
And since the fighter-only feats are bad, and everyone can get the other fighter feats, this winds up making the fighter a pretty poor class. Fighter 2 is OK; a feat every level’s kind of useful, though usually only those who are really desperate for feats should really go that route. But after that, the fighter class offers very little. Therefore, I strongly suggest multiclassing, taking some fighter levels, some barbarian levels, maybe some ranger levels. Horizon walker’s a pretty good prestige class. Basically, you take Fighter when you need a feat; you don’t take Fighter just because and then figure out what feat to get.