How to protect my Google Account? I am very concerned with security of my Google account in case I lose the phone (as in: lose it, have it stolen/robbed, etc.). Right now it seems that whoever grabs my phone will also have full access to mail, calendar etc.

I would be perfectly happy to sync manually and/or have a password prompt every time I try to sync, but I don't see this option.

How can I protect my account? Is screen lock any good? How hard is it to bypass it?

The phone is HTC Desire should it matter.
Instead of entering a password every time you sync or access your mails - which will also be more insecure, because you enter the password often and in public - think about a good screen lock (PIN or Password) and a remote wipe solution.

Changing your Google account password is always a good idea in case of a stolen Android device. According to Oleg Ostroumov comment, the device will stay logged in for ~hour and then request a password.