Jaagjah wrote:あなたのあるくの = You're walking?
This is "Your walking." The の after あなた marks possession, and when の follows a verb, it turns it into a noun (although it can be used to mark a question, but given that the walk is being possessed, it makes sense to me to interpret this as a case of nominalization, even if it is a sentence fragment).
A: "Your walking"
B: "What about my walking?"
A: "It's strange."
"You are walking" would be あなたはあるいている。
~て+いる form of a verb means that you are in the state of that verb, which is similar to the present participle function of -ing in English, which denotes a continuous action. In this case, the two match up very well: "I am in the state of walk" is no different than "I continue to walk." But if I used 広げる: to open, "I am in the state of open" is very different than "I continue to open."
Jaagjah wrote:私行くのが私のへや。= I'm going to my room.
Or would it have to be:
私のへやにいく。
Your first sentence lacks a verb due to 行く being nominalized by the の.
私のへやにいく = I will go to my room.
私のへやにいっている = I am going to my room.
Jaagjah wrote:なんははなしたんだか。= What're you talking about?
There are a lot of ways to say "What're you talking about?" I'm going to remove the んだ here for simplicity's sake, because it's emphasis and could be translated in a bunch of different ways depending on context. This is "What had said?" Changing the は to a を makes なに a direct object instead of the topic doing the verb.
なにをはなしたか = What was discussed?
For "talking," we need to use the ~て+いる form.
なにをはなしているか = What are you talking about?