iPhone apps question?

I have an unlocked iPhone that was unlocked by Apple. My company does marketing for them, long explanation! lol The phone is also jailbroken.

I downloaded a free app via iTunes but did not put it on my phone yet. Here are my questions:

1.) Can I just sync it with my phone as I do with iTunes music and it opens?

2.) Do I need to download another program to make it work since my phone is unlocked?

3.) Is there a risk that this could brick my phone?

Thanks for any help!

PS- again my iphone was NOT unlocked/jailbroken illegally and I still have Apple's warranty.