British people prefer to pronounce the words correctly, American people shorten them very often. But if you write an offical letter it is better to use. " want to "

they are the same. wanna is informal version of want to. I, if in your place, would have used want to. thats proper,formal and better english. hope it helps. :)

"wanna" is mostly used in spoken english

If you use "wanna", people won't take you seriously. It's lazy English. Avoid using it.

What everyone else has said is correct. You'll also encounter the same thing with the following words: "going to" -> "gonna" "could have" -> "could've" -> "coulda" "should have" -> "should've" -> "shoulda" "would have" -> "would've" -> "woulda" Again, this usually applies only in spoken American English but it's good to know because some singers will write their song titles or lyrics this way too.