I think the answer to obstacles (1) and (3), and part of (2) is reading the short book titled, "Getting to Yes" by Fisher and Ury. It is the "bible" of negotiation and conflict resolution.
Learning the easy skills in this book will pay dividends for the rest of your life, not just in this situation. It teaches you how to negotiate based on merits and shared interests or principles, not staked out positions like "we don't allow telecommuting." I have employed the techniques from this book hundreds or even thousands of times in my life, it is very effective.
I think you can make a compelling case irrespective of all the anticipated objections, don't sell yourself short. And the fact that you've already had the foresight to predict some of those potential objections says to me you're already on the right path.
Find and present to your employer the ways you think they will benefit from the arrangement. Then listen to them and any objections. Deal with the objections by appealing to their interests. Tell them, "I've heard your objection <X>, it makes sense to me. What solution could we find to effectively deal with that?"
It doesn't have to be done all at once, it can be a work in progress. You might say, "I've heard some of the problems you foresee with telecommuting; I'd like to take some time to think about them and come back later with some possible ideas, would that work for you?" In short, keep them engaged in the process, enlisting them as a mutual problem solver.