Ok, I will play devil's advocate. Have read all the OP's posts but not TWT.
Coming from a complicated family myself I can say there isn't a right or wrong answer to this. People may question judgements your partner has made in the past about his involvement with children he didn't know at the time he has fathered, but I think wanting some involvement with them now shows that he has matured with time (which is something that not everybody does). Big secrets can take time to tell, the fact that he wants to share them now after knowing you for 2 years may indicate that his trust in you has grown, not that he is and always will be an evil SOB.
Bear in mind that parenting a 19/20 year old is not the same as parenting a toddler. They are adult now, and hopefully have a lot of responsibility for their own life. They may be mature and responsible people who don't want to be an emotional and/or financial drain on their biological parent. You won't know unless you meet them (and only one of them sounds currently interested).
It sounds as if you are a wonderful step mother and your mature outlook could be a good example for some of the other threads I have read on MN.
Reversal of vasectomy is not something men usually do lightly, again this indicates that he really would love to have children with you.
How many children is too many? The question is different for everybody. Nowadays 2 children is the average....but I have a couple of friends with 4+ children who seem deleriously happy (if slightly insane IMHO!!).
Decades ago it would not be at all uncommon for people to have 5 or 6 children and if both parents had decided that 'family' was what they wanted from life then that's absolutely fine.
However I do agree with other PP that at the moment you need to decide what YOU want. If you go down this route of having children with this man you are going to be tied in somewhat to a large blended family, which will be all the more difficult if you decide later on to have a major career change (wanting to study, or work away) or if you want to do exciting travel, or if you decide at some point you just want a 'simpler' quiet life!!
My advice would be to take some time by yourself to decide what you want, maybe take a step back from him for 3-6 months and possibly live by yourself, possibly date a few other people. You still have plenty of time in terms of your age.
If you truly love eachother then the love will still be there in 6-12 months time.
Some counselling, individual or together may also help to resolve some issues.
Hope my alternative point of view helps!