Note that when speaking of what somebody else wants you should use the -がる form. E.g. たい→たがる. Basically you shouldn't say "She wants to ___" but "She looks like she wants to ___".
In asking questions the direct 〜たい form is fine.
In modern Japanese 〜たい generally takes を with が being used for emphasis when strong feelings are involved.
Formed from noun + wo / ga Verb-masu base + tai
Vm = Verb -masu base
Could someone explain the な〜 at the end of the example sentance?
な〜 is a collequial sound. "ya know?" A little bit like "ne" but more plain.
な〜 is express your feeling by put 〜 written sentence. You can also write 見たいな。見たいな〜。見たいよ〜。見たいね！
From what I've heard (and seen used), 〜たい / 〜ほしい is used even when referring to other people, because it's regarded more polite than 〜がる forms. This might be limited only to 2nd person, though, I'm not completely sure.
I've found an example, notice bottom-middle panel in http://mathrick.org/files/03_032.jpg . 用があるからちょっと顔を出して欲しいってさ。 "He had some business for you, so wanted you to show up"
Mathrick, the sentence you've provided is a quotation, as indicated by the quote-marker って (って is a common abbreviation of と). Therefore, in your example sentence, it is appropriate to use the first-person form of 欲しい, because the speaker is quoting/paraphrasing another's first-person remark.
Why use 買いたいんですin ex #5242 but したいのです in ex #6529? Wouldn't 買いたいです and したいです be correct?