I've certainly found that in fast games I just reinforce my own mistakes over and over again. The things you learn won't really sink in before you implement them in long games.

Don't worry too much about the openings. At a beginner level you should be fine playing the opening as if it were a special kind of middlegame.

Your books are probably fine. I first started going through Polgar's Chess which has a huge number of mate problems. It's great except for a tendency to have too many sacrifices as first moves, especially queen sacrifices. The book I use now (very seldom, sadly) is Blokh's Combinational Motifs (or something like that).

I've also heard "The Art of Checkmate" by Renaud and Kahn is a great one, but I haven't checked it out yet. Yeah, I have to start playing longer games...

In case you're still interested, the trial issues appear to be here.