Is Contact module the right choice for multiple ask a question pages? I have a set of pages already developed. For each page I need to add a new page with an "Ask a Question" form to let end users contact via email the corresponding page owner.

I tried the Contact module but it doesn't seem the right choice.

One of the requirements is to hide the recipient email address from the user.

How can I create such a customized form and be able to set a different recipient on each page? Do I have to create a new Feature?
Depends , you can use the webforms module to create custom forms it's better suited for creating forms than the contact module