First things first, thanks for all the replies, I really appreciated them all.

I had already checked the dropouts alignment but I'm acquiring the stuff needed to improvise a DIY tool somewhat similar to that Park Tool makes (albeit a lot more ghetto!)

As for the wheel, it's out of true, and it does wobble left and right of its own axis but not the tube's. I've tried to adjust the spokes (many were loose) but that I'm totally new at this and had little or no success. I'm planning to keep the old rim to practice on it some more.

Also, before wasting more money on this bike, I wanted to know if the frame was totally out of whack or this was something more or less acceptable. Now I know the latter is my case