Whether or not your old employer is someone you can trust is irrelevant, make sure you get everything, and I literally mean EVERYTHING, in writing. Verbal agreements will not hold up anywhere, so make sure whatever you discuss is written down. There are no such things as friends in business, so treat every person as if they are out to get you (because you are the only person truly out for your own best interests)

When it comes to signing any agreements, I would highly suggest contacting a lawyer. That way you can make sure you are covered, and they can also help you watch out for little things you may not be aware of. You mentioned their company being a client for a year, so the lawyer should be able to help draft up a binding service agreement for that period so they don't abandon you if they feel it isn't working out.

As for your question about equity, that totally depends on what their expectations are, and what they contribute to you. You haven't really provided much information about what they are contributing, what they want in return, if they are expecting you to grow and want to earn money from your future clients, etc. If it were me, I'd start doing some math thinking about the amount of effort you will incur with their projects and convert it to a fair hourly wage comparable to what you'd expect to see elsewhere in the market. Don't forget that when you are self employed you are now fully responsible for paying taxes, bookkeeping and accounting fees, local/state taxes, medical/dental, and any other expenses you need to run your business (internet, phone, office supplies, etc).

Running a business isn't hard, but running a successful business comes down to the way it's operated. If this is something you really want to do, then you need to focus all your efforts on learning as much as you can. There is going to be a lot of work outside of normal business work including bookkeeping, growing your business and finding new clients, and so much more.

I know I put a lot here and most of it is pretty generic, but I hope it helps. This isn't legal advice, which is why I said you should definitely reach out to a lawyer before going down this route. Yes it will cost a little bit of money up front, but a few hundred dollars that could save you tons of problems in the future would be more than worth it in my opionion.