1) For an experienced amateur with a few years of visual astronomy experience plus a year of astrophotography experience then yes, it can be done if your budget can handle it. For an observatory that can run unattended from a remote position expect $20,000 for the minimum outlay needed to do it right. That's if you do much of the observatory construction yourself. Most budget far more however.
2) It is one of many solutions.
3) This depends on what your mount is, what else you need to control, what fail safes you need -- see a storm coming and shut down, power goes out at the observatory how do you shut it down?, how do you control the roof/dome, what type of sensors are you using, what type of astronomy are you doing, do you want to lay out an evening's data collection so it will run unattended going from object to object on its own etc. etc. etc. I get the feeling you haven't thought out all that's involved here.

Highly experience amateurs with near unlimited budgets are doing this. From the lack of needed info in your questions I have to doubt you meet the first requirement.

Rick