I bought mine in my landladys name as I couldn't get a Thai license due to offices being closed because of Covid. I have insurance in my name. I have renewed the tax without problem. I'll probably leave it in her name until I sell it now. You'll need the Compulsory government insurance with minimum coverage and you can get further cover separately. If you want 1st class insurance, there's not many doing it for scooters, only big bikes. I used MSIG. Not sure about leaving country. An agent can get you the residence certificate for a fee.
We got married here in May. We had to get the affirmation from the UK embassy in Bangkok. We then used a translation service in Bangkok who did everything and sent the paperwork to us. You then take this to your local Amphur.
What I would check is, how long it takes with your Amphur, it took ours 2 months. We had to have a police check in Thailand which takes a few weeks for the police to send it around. Here, the mayor got involved, so everything had to go via him. It's a couple of hundred baht for the certificate.