Good question. 1st question: I might still play them, but I would be more specific about the rules. One guy who had a lot of money wanted to play me a few hundred a rack of one pocket. We had played a few times before and I was up quite a lot on him. But this time involved a much larger spot. Now, I had a good hunch that he wanted to just get up 2 games on me and quit. I saw him do this to another player. So I told him before we started, only the loser can quit (or if we're even), otherwise I won't play. He agreed to the terms. Incidentally, it was a good thing I made that stipulation with him. He got up 3 games on me, and I knew he wanted out. I fought my way back, and he immediately quit at even when it looked like I would continue to win. I figured he was worth this risk because he had a lot of cash and the potential to go off. I wouldn't even consider this type of risk of being quit ahead on with someone who is known to be broke.
On a smaller scale, I had a regular game with a guy for 50/set. We would probably play once every other week or so. After a while, I realized that I couldn't get into his pocket. If he lost the first set, he would quit. If he won the first set, and I won the second, he would quit. If I lost the first set, and the second, he would then say "last set" to ensure he would end up the winner. This pattern of his took some time to determine, because of all the possible scenarios. But what I saw was that unless I won the first set, I wasn't getting into his pocket. And if I was down, the best I could do was get even, if that. So I made the decision to stop playing him. It wasn't worth the hassle. There was no future with him, because he was only a 50/set player and the effort to get into his pocket was not worth the small reward. Now, some of you might say "well if you keep winning the first set, what is the problem". But this particular case was a close game, where it truly was an even proposition as to who would win the first set. But because of his quitting habits, it was just too tough to beat him.
I didn't quite understand your last two questions in their entirety.
I am no expert by any means. I have both lost and won my fair of small and big bets. So keep that in mind...
Speaking of types of players, some players are in it for the long haul. They just expect when they match up it will be all night long, or till someone is broke. I was one of these players, and many others around me were too. Knowing that, it often took me a while to warm up, because I knew I would be playing all night. It also brings stamina, and decision making into the game much more than playing just one or two sets. I often felt I had the edge in a long session. That is another reason for not wanting to play just a one or two set player. Now, this type of player rarely exists anymore. The action in our room is all but dead compared to 10 years ago, and even 5 years ago. And any action that does take place is very small, and just one or two sets. And from what I read here, I take it it is similar in other places.