Mac Newbi questions

Hello, I've had my iMac for a few months and I love it, I just have a few quick questions.

1) Every time I go to install something it asks me for my password, as I don't have a password all I have to do is press ok and move on but its kind of annoying.

2) When I try and shut down the computer and my Wifes logged in it forces me to enter her username and password (once again she has no password) but I still have to enter her username. Thats really annoying.

3) sometimes the computer is really stubborn about shutting down or logging out while in my profile. I go to shut down and it A) does nothing or B) goes to just my background picture only, (No dock, desktop icons, or upper menu bar) times out and gives me and error message telling me Safari caused and issue with the shut down. Even if I close Safari completely (Safari menu - Quit Safari) it still does it.

If anyone can give me a hand with the few small issues I have that would be great.

Also one more thing. Does Apple have free phone support for the first 90 days only or is it for the full first year.

Thanks
Jordie

Try these suggestions;
(1) Disc Utility, repair permissions
(2) Reset Pram (restart holding down option+command+p+r keys until you hear chime twice, then let it start
(3)As for users, tell your wife to log out when she is finished with the computer!
(4) Have a password for yourself as admin and set your wifes account as standard so you have responsibility for the software etc.
(5) First 90 days