Will you find more weapons suited to your character?

Right now my character is the sharp-bladed weapon expert, and I'm halfway through Act 2 and I have not found a single firearm (but many knives, etc). If I choose the firearms expert, will I be able to find a guns or is it still too early in the game?

Are drops tailored to the character's strengths?

As far as your first question (will I find guns as the firearms expert), I'm also in the middle of Act II as the firearms expert (Purna), and can say that previous to adventuring into the city I'd only ever found two guns (a fairly bad pistol as a quest reward in Act I, and a single-shot rifle from a chest in Act II). However, the city seems to have numerous locations with respawning non-zombie baddies carrying a variety of medicore pistols, and tons of ammo. Additionally, Purna's fury allows her to draw a firearm and fire six shots, regardless of whether or not you actually have ammo (and it won't consume any of your ammo). Additionally, in Act III, numerous enemies will wield both rifles and pistols.

As for your second question (are drops tailored), it seems the general consensus is that they are not. Acts II and III are filled to the brim with firearms, and you can get ammo mod recipes for all three types of guns (pistols, shotguns, and rifles).

Drops are not tailored. There's just not many guns before act II, and even in act II, only punks drop guns/ammo, and they're only located in certain parts of the city. I'm not sure if they become more common later on, but I assume not, guns/ammo are supposed to be rare/precious.