HI Brian and welcome to the forums!
No not in all cases do you support everyone, clearly you cannot bring everyone to the US but you will be asked for money eventually for them. OR you would be asked to be a baby godfather which = money! Or best man of the wedding = money.... etc etc.
Not outright asking for money when you were helping out when you did, well that might just be because you were doing enough voluntarily but I can pretty much guarantee she would ask eventually. Being lazy and not learning english - again not a big surprise. They see it as no big deal, they won 't need it anyway...... How wrong that is.
We have said this before and it bears repeating - the family is friendly and accepting - that is partly the culture and partly that you are the great walled who has descended upon them to help them.....LOL Not unusual.
I fully understand why you would be attracted to Dominican women. They are NOT all the same and I hope you find what you are looking for.
Age - I have heard endless stories on this one. One of my employees had a cedula that says he is 27. In reality he is almost 29. Dad didn't get around to registering him for almost 2 years...... not unusual at all. Differences in ID dates etc - again not unusual. And no one seems to care, that would take work to fix it and probably money too.