You get what you pay for. Some hand cappers suck, and others work without a problem. Some bottles seem to work better than others for me as well. One thing I do is if a cap doesn't feel like it's going on well once I start to put some pressure, then I ease up, turn the bottle 90 degrees and give it another go. Usually that does the trick.
As far as the O2 caps go, from what I understand you're fine. They do become activated once they're wet, but it takes a while for them to start working (like up to 48 hours, IIRC). They won't get all used up in an hour or so of bottling.