No. For medical services, you don't get any privileges over and above what a tourist gets, while on a DTV. At many public hospitals, Thais pay less than foreigners. At some of them there is a 3 or 4 tier pricing system. While on a DTV, you'll pay the highest price out of these tiers (work permit holders pay less, while migrants from neighboring countries pay even less and Thais pay the least).
At private hospitals, in theory at least, everyone pays the same but it's recommended you're insured.
Not just that, but most banks will charge you a withdrawal fee on their end (AUD / CHF / USD/ EUR 5) usually and a percentage charge of up to 3-3.5% of the amount withdrawn.
Only a small handful of banks refund these charges.
Thus withdrawing money from a Thai ATM can be very costly using a foreign card.
You do. I've never come across an international flight where I didn't have interaction with a check-in agent. Even bag drop for internet check-ins have an agent which then checks your passport and visa.
Well, normally I would show them my visa at the check-in counter and not be hassled again afterwards. It does depend on your situation; basically, you should be prepared to show it again though it shouldn't happen.