(FYI, I'm one of the owners/developers of FastMail)

1. Just add addresses to your address book to whitelist. Also make sure you use Report Spam/Report non-spam on enough emails (200 of each) to activate your personal bayes db (see the Options -> Spam/Virus Protection near the bottom to see how many of each you've already learned)

2. At the moment, you do have to explicitly add body: to a term to do a body search. The first time might be slow as it indexes your email, after that it should be faster.

http://wiki.fastmail.fm/index.php?title=NewInterface#Enhance...