ADOBE sign API

We need just Digital Signature API. As we are developing web application(c# MVC net framework 4.6) for our customer we are looking forward to call API from our software so that we can directly use Digital Signature.

I have following questions

1) Can our application user sign PDF document at different location on different time?

2)  Are these API will host on our application server or  PDF to be signed will go to ADOBE server?