The short answer is "Yes." Persits software makes a component that will do all of this quite easily. http://www.asppdf.net/
is the site.
I am doing exactly what you are doing, though using the older version for Classic ASP, and it works great, including the e-signing. (We actually save the PDF as a file and then attach the file to an email we send to the client. And if they have a fax number we fax it as well.)
You *can* build this yourself in ASP.NET code, of course, but it would take you many many more hours than the cost of the product. Just creating PDF is not trivial and modifying existing PDF (i.e., for filling in the form) is even harder.
The product costs $299 US for a single server, which is probably all you need for the typical internet situation.
I have ZERO financial interest in this. I just think it's a good product that is well worth the price.