Ok. A tourist visa is valid for 90 days from issue date. That means you have 90 days to wing your way to Thailand.
On entry you’ll get a stamp for 60 days stay on arrival. So you arrived yesterday and got a stamp for another 59 days (arrival day is day 1). That is a correct stamp for that visa entry.
The TDAC has nothing to do with any visa type (or exempt entry). All foreigners fill it out regardless of what visa they hold. It doesn’t give you any time on entry. Your visa gives you that. Visa exempt is currently 60 days.
No one can give a definite answer to this as it’s up to an individual immigration officer to decide.
You should be fine, but if questioned have the three proofs - 20,000 baht or equivalent in CASH, proof of accommodation for the first few nights and a valid ticket out of Thailand.
In Phuket you can use one of the three immigration offices. Phuket Town - most busiest, Patong Beach - not so busy or Blue Tree office - least busy. All have photocopy or photo places onsite or nearby.
You’ll need your passport, a copy of the passport photo page, a copy of your entry stamp in to Thailand, a passport sized photograph, a filed TM30 and fill out the forms TM7, STM2 and STM9. All forms are available onsite. Use a blue or black pen.