Did she even tell him that she cheated on her the father of her first child with me, & cheated on me with someone else?
Probably not and instead made up a story to justify her behavior
Did he even ask her why we broke up? Does he even care?
See Above
What happened to his fiancee?
Not worth thinking about
Did this relationship actually start long before & I was just not aware?
Probably not worth giving it a lot of emotional energy
Is he yet another rescuer, knight in shining armour type, who has been sold a sob story about how terrible I was?
You may be right. Or maybe he is simply easily manipulated.  :)on't give it too much energy.
Is this guy treating her better than I did?
According to "her" now? I am sure he is wonderful but we all know how it goes in the end.
Does he understand her better than I did because they come from the same cultural background?
Unless this new guy is an expert in dealing with BPD he is going to go the same route in likely even a shorter period of time.
Has she been changed by our break-up?
Not unless she has been getting serious and prolonged treatment which most don't
One of our mutual friends told me she has stopped drinking & smoking, says she wants to settle down now, no more messing around... .
Well with three? kids she better but because she suffers from a personality disorder, unless she gets treatment, not much will change.
Has she even shown him that "other side" of her yet?
It eventually comes out. It always does in the absence of getting professional help.
Will he be able to handle it when she does?
The odds are "no" unless he is Gandhi or the Dalai Lama
Why is he always at her mother's house when I'm picking up & dropping off our kids?
Not worth the energy. What is important is harmony when you are picking up/dropping off
Why does she seem so jittery when I'm there, seemingly not wanting me to see them sitting together on the couch or whatever, yet she posts pictures of them hugging & all that on face book?
Because she cannot deal with her own feelings
Will she neglect our 18 month old daughter now that she's so focussed on this new love of her life?
Spend as much time as you can with your D.
Last weekend when I fetched her, uBPDex was nowhere to be seen (left the baby with her mother?), baby daughter was not bathed & her nappy was soaked through to her clothes, same runny nose & cough she had 2 weeks ago when I last saw her... . :-(
Will she be more agreeable to letting me have custody of our kids now that she wants to start a new life / family with him?
Am I crazy for thinking about all this crap instead of getting on with my own life?
Aaaaargh!
Outside of your parental responsibilities, worrying about the other stuff is not going to help you moving forward, or being a great dad.
Peace