Yes.
Check the prerequisites. Power Attack needs a Strength 13, while Piranha Strike needs Weapon Finess, which is interesting only if your Dex is greater than you Str, so we can deduce that the latter is intended for Dexterity-oriented characters, the fluff text incidentally says one using Piranha Strike provokes "multiple, minor wounds".
For a more complete answer, Power Attack doesn't say anything about light weapons, but it does say that you can use this feat with a natural weapon, and natural weapons are considered light weapons.
Besides, if you couldn't use Power Attack with a light weapon, the description of the Piranha Strike feat wouldn't explicitly tell that
This feat cannot be used in conjunction with the Power Attack feat
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.
Best Answer
Weapon Focus is absolutely a bad feat. In fact, it’s even possible that this was intentional on the part of the system’s designers. It is frequently used as a “tax” for stronger feats or prestige classes.
This is pretty atrocious design, and I can state unequivocally that 99% of those taxed options do not deserve such a tax.
Also, for reference, the entire “chain” of weapon specialization feats are similarly poor. Actually, most of them are a lot worse, requiring Fighter levels and not often being used for prerequisites. The exception is Weapon Supremacy in Player’s Handbook II, which is fairly powerful, but comes way too late and requires way too many things (including Fighter 18).
Your Initial Suggestion
It’s clearly better, but I’m not convinced that makes it good. Ideally, feats should be better than just a straight numerical bonus. The +1 damage is almost meaningless, and +2 to attack is fairly minor as well.
So while better, this isn’t good.
Your Second Suggestion
Better, in that the scaling bonus matters a lot more. Problematic, in that it fundamentally throws off a lot of calculations – attack bonuses already scale much faster than AC, now they’re scaling much faster than they used to. You almost have the flip-side of the problem now: for a lot of builds, Weapon Focus becomes required, because as boring as it is, being without that huge bonus to attack is putting you on a different playing field. That bonus is larger than the difference between medium and full BAB at any given level.
My Suggestion
First of all, I don’t care for the entire concept of Weapon Focus; few characters are going to care very much about the type of weapon they are using most of the time. Most will use weapons all of the same type because they chose that weapon for a reason. And all this accomplishes is giving them extra trouble with damage-type-based DR (e.g. DR 5/Piercing or whatever) that forces them away from their favored weapon.
So my personal preference is to simply eliminate the entire line of feats altogether. Anything that required them in the past, simply loses that requirement. I can imagine that there are cases where I’d want to tax the player, in which case some other feat would take its place.
But if you insist on going this route, I’ want to add features that are actually useful. Not just bonuses, but the ability to use new features of the weapon. This also avoids giving too much of the simple attack bonus, which throws off a lot of calculations.
So something like this:
Analysis
This feat is designed to improve the basic power level of melee in the game. Weapon Focus is a Core feat; lots of other feats and prestige classes require it. Now, it’s a feat most melee probably wants: the bonuses for using a weapon from these groups is pretty significant. I’ve tried to favor the weapons that are inherently weaker with stronger Weapon Focus benefits, but that’s tricky.
Granting a feat as a part of a feat is a weird thing to do, but what this basically ends up doing is providing different requirements for those feats that were previously also very tax-y. Pay two taxes with one bill, I suppose. Things like Rapid Reload (necessary to use crossbows seriously) and Combat Expertise (requirement for several of the Improved combat maneuver feats) are necessary but not that good (crossbow+Rapid Reload still is not as good as a bow, Combat Expertise is a terrible feat on its own). Cleave is the exception; Cleave is a pretty weak feat, but usually it just gets ignored, rather than becoming a tax. On the flip side, axes and swords are the best non-reach weapons, so that balances out (sort of).
A note on Knockout, and the Sicarii: flat-footed is not the same as denied-Dex, and unaware in a surprise round is even more difficult to get. Knockout will, at best, drop one target per encounter, and most encounters you won’t really have that opportunity. Sicarii works a bit more often, but you have to work at it more than Sneak Attack: no simply flanking an enemy and going to town.
A Side Note
In discussing this suggestion in the comments, I was reminded that Legend does similar things with its weapon feats. I do recommend looking to Legend for ideas in that regard: for the purposes of feats, anyway, Legend material can be ported back to 3.5 relatively easily.