Can an unlocked iPhone download from AppStore and iTunes?

[Milkshake]

Hi I'm a newbie on iPhone 4. I want to know if my unlocked iPhone can download apps and songs from AppStore and iTunes? I'm afraid to download anything as it may get locked or something..
I also have this Cydia application in my phone. What is it? Is it safe to use?
Thanks everyone for the help.

 

[DannyBoy]

Yes, it's fine to use it won't lock or unjailbreak.

 

[Milkshake]

thanks a lot for the info! now I can fully enjoy my new iphone 4