n he somehow talk his way out of it?

He does have some responsibility to do the work. If he doesn't he has breached his contract with you and may owe you a refund of your fees.
Truly abandoning a client and neglecting his or her case is also a violation of professional ethics. This is a pretty minor offense compared to the offenses involving idea theft if it happens in isolation, which might result in a minor slap on the wrist like a private reprimand that would be held against him if incidents like this surfaced again in the future.
But, this routinely leads to an attorney being disbarred (often on an uncontested basis) if an attorney one day just stops working for almost all of his clients and walks away from his practice (often due to a psychological breakdown, despondency after a divorce or an affair, dementia, untreated mental health conditions, a personal tragedy in life such as the death of a spouse or a child, or substance abuse). There is a small but persistent trickle of cases with that fact pattern.
It is hard to know from the perspective of an individual client if he just got busy and overlooked a case or two including yours, or if he totally shut down or walked away from most of his practice.

Can I get a court order requiring him to do the things he offered to
do in the email that I agreed to, for the price we agreed to?

No.
You can sue for the money damages you suffer from his breach of contract (but probably not speculative lost profits), but you can't get a court order forcing him to do what he promised to do (among other things, it would violate the 13th Amendment to the U.S. Constitution for a court to do that).
Idea Theft
The second issue is what happens if your lawyer steals your ideas.

Regardless, I'd like to know what I can do if he does not complete the
work and starts a company that does the same as what I had planned to
do.

This is very unlikely and a very unwise choice for the lawyer.
An Analogy
In terms of likelihood and severity of consequences if a lawyer does so, this would be o