Yes it will as long as it is GSM and it is unlocked
You can, but it costs extra money from your account.
No - usually the mobile networks will do all the 'hard work' for you.
Most people in the US have a cell phone.
The country prefix for Romania is 0040.
Probably, it depends on where your phone is actually from because the frequencies may not be the same. However, Sprint is a major US cellular carrier and it is likely that your phone will work fine.
In the US it is only AT&T.
If the phone is a world phone that supports overseas frequencies, yes.
If the headphones work on a PC in the US, then they will work on UK PCs. However if your headphones come from a cell phone, then they will not.
Yes you can if you are on a mexican sim card/network. It is possible to text if both are on the same us network but you need signal for that network.
Verizon wireless, Sprint, and ATT
yes
Only if it unlocked and support Quad band GSM 850/900/1800/1900.