a visa allowing you to live in that country. Not necessarily "permanent". It can be a paper in your passport. It can be a card (like US green cards or UK BRPs). It can be electronic like Australia (the airline's computer "talks" to Canberra's computer and confirms that you're good to go before check in can be completed)
yes ... you're right that the rules (or lack of them) can be confusing. The other confusing thing is that what rules there are can be interpreted differently by every immigration officer! In general they're not against someone with a tourist visa coming as tourist. What they're against is someone who uses consecutive tourist visas (or visa exempt entries) to LIVE in thailand rather than to VISIT.
Bring proof of where you stay (a letter of invitation from your girlfriend in your case) ... bring a ticket that shows you will leave within the validity of your visa ... bring 20,000 baht (or equivalent) in cash.
Those who are being refused are those who are in and out all year, who try to fool the system, and don't have the correct visa.
I would carry something from the parents just to be sure. Many countries enforce this strictly, many enforce it intermittently. South Africa was the most famous (and problem-causing) recent example.
Hello. Airline staff here. My job is to be on the line when check in calls with passport and visa issues.
Yes, if you have this set of circumstances, we would refuse you travel.
Yes, you need to produce a ticket proving you will leave Thailand before your visa expires.
If Thai immigration refuses you, the airline MUST fly you back (bumping off and compensating another passenger if the flight is full). Also the airline would be fined for allowing you to fly.
Yes, some people get away with it ... well done! Don't count on it.