Different types of nominalization

Question

I recently learned that you can use a verb stem or its i-stem to get its noun. Before that I learned you can nominalize a verb with base form + こと. I looked at different sites to understand the difference and now also learned about base form + の. Unfortunately nothing I have read so far helped me to grasp the difference, if there is any. So I thought, I may ask here with near-identical example sentences:

• 映画を見に行きたい。

• 映画を見ることに行きたい。

• 映画を見るのに行きたい。

First question would be if all these sentences are even correct and if so, what are the differences and which one does sound more natural.

Answer 1

映画を見に行きたい。

This means "I want to go see a movie.

映画を見ることに行きたい。

This means "I want to go to watching a movie." (見ること means "watching", literally "the fact of watching", so you're saying you want to "go to the watching (of a movie)"

映画を見るのに行きたい。

While it can mean the same thing as above, most people people would parse this as "I want to go in order to see a movie", with のに being here translated as "in order to", with nominalizer の and target に.

The first sentence sounds natural and correct to me. The second sounds nonsensical. The third one sounds like you're saying something different. The issue is that 見に行く means something very specific. If you want to see how the nominalizers differ from one another, I suggest you check this.