-ているんですか？

This is another form I've heard a number of times - I have no idea what it means! What's the difference between these?
田中さんはニューヨークに行っているんですか？
田中さんはニューヨークにいきますか？

Nominalizing

I'm interested in learning and getting comfortable using the nominalized forms of verbs, using things like ーこと and ーの. One common form I've come across is for stating whether you've ever done something (I'm not sure if I've got this right)
ロンドンにいきましたか？いいえ、いくことがないです。
Or,　おもしろい人とあうのが好き。(I like meeting interesting people)

I think I've also seen a version using the plain past (instead of the dictionary form): 行ったこと - what does that mean? What is the difference between the two?

If I'm not mistaken, there is also a nominalized form using ーとき ('times'). Like, べんきょうするときにおんがくをききます ("Times when I'm studying, I listen to music").

さとうせんせい、ちがいますか？