If you hold a passport from GB or Ireland you don’t need a visa for 90 days as Stepehen explains. Just get a cheap ticket out within the initial 60 days if you’re airline ask for it.
Only two months counted in days, so 62 days is fine. You don’t necessarily need two full calendar months. The 19th one month until 18th next month gives one month.
You could apply for a 90 days Non O based on marriage through the Thai embassy in London before you go, put 400K baht in a Thai bank account two months before you apply for yearly extensions of stays. If you also purchase a multiple re-entry permit you’ll be able to come and go more or less as you like.
Alternatively a Non O based on retirement and bank 800K baht for the first year extension of stay and switch to monthly income for the second year by showing proof of twelve months consecutive transfers of min 65K baht.
If the landlord registered you electronically, you should get a receipt or screenshot of the registration. You could do it yourself at the immigration if you bring your lease contract and a copy of the landlords housebook and ID-card. It’s the landlords responsibility but your problem if it’s not done.
Yes it should be enough if you also have a receipt of your TM.30 address registration at your immigration. The owner of house should register you on a TM.30 within 24 hours of your arrival.