What's the deal with writing ha for wa? Is it not because there are two symbols for the same sound that 'ha' needs to be inputted as 'ha' rather than 'wa' when using a keyboard to write hiragana? Phonetically the sound is still 'wa'. Is writing 'ha' a common convention when using romaji?
Using 持っている is fine; eg PSPを持っていますか, ie. do you have PSP?
PSPがありますか means "is there a PSP?".
I daresay there is no need to use personal pronouns in either case; it might sound a bit unusual, to say the least.
I'm also tempted to think that if you were going to ask someone's name using あなた, you might drop the お in front of 名前. ie. あなたの名前は何ですか vs. お名前は何ですか。Still, I can't help help but feel that the use of あなた in this case is anything but polite.