As much as I'd trust any other open source project.

I hear you. I've had far too many problems with stupid and unnecessary restrictions on password strength. I use a 32 character password of all printable ASCII characters wherever I can.

For all intents and purposes, KeePass's encryption cannot be broken. The only "what if" is if your master password is somehow compromised, but since that should be exceptionally strong and never written down, that shouldn't happen!

Use a password database like KeePass and have a long, unique, completely unmemorable password for each site you use (except perhaps a few of the more common ones you're likely to access regularly). If you have a smart phone this is even better because you can carry your password database around with you and have it sync automatically with your computer. Remember that having the same password for many sites not only means that if it's bruteforced for one site it's compromised on one site it can be used on others, bu also that if a site itself might be malicious enough to store your log in details and test them on other sites. See xkcd.

The on-site data centres at CERN are actually terrible when it comes to cooling (at least they were when I went there). I was expecting the server rooms to be low-ceilinged rooms with AC units good enough to keep the rooms at least chilly, but they were actually swelteringly hot, and one of them seemed to be in an old warehouse with very high ceilings.