no you dont need wifi you can unlock them in offline mode just when ever you go back online on steam all the achievements will unlock at once so they will all have the same time stamp. also steams library has never lagged for me on my computer.
It might not lag for you, but it does lag for me and many others. Painfully so. No, there isn't a way for me to improve it without also getting rid of much desired features.
I largely agree with the achievements part of your comment though. There are some games that don't register achievements in offline mode, but most do AFAIK.