These are the only connections it makes:
Using premium Login?: Connects to Mojang login server using ssl
Downloading "Minecraft Release" versions?: Connects to Mojang servers
Downloading launcher updates, JavaPortable, and 1.7.2liteloader(my custom modpack): Connects to Kraftzone.net
It doesn't do any automatic net connections, any connection made will always proceed a button or dialog prompt asking you beforehand.
"keeps passwords completely safe?"
Nope, if you store your premium login&password with my launcher, it saves that info locally to the file "Minecraft Launcher.xml" that will store plain open text password. I could encrypt it, but anyone who runs the app will be able to get the password anyway because there is a Show/Hide password button.. This minecraft launcher is for really my own convenience and portability, if you are worried someone might use your computer and steal the password(s) then don't save login/password, you can just enter it everytime you 'Launch'
I can encrypt the local username/password, but just like mojangs old launcher anyone could still get the real username/password. Its pretty much why they remade there minecraft launcher, and force people to relogin to there minecraft account.
btw new launcher update to try, its still beta as explained in the post:
http://kraftzone.net/forum/index.php?topic=1234.msg11988#msg11988