US or Standards edition- which do you prefer and why?
I prefer the Standards edition, but I really only compared the 2 in the K level. I liked the graphics more in the Standards which helped with some of the problems. Sometimes DD was confused (US edition) because the picture didn't look right, or it was an object that kids in our area wouldn't associate with. I also liked the fact that the Standards edition has more work pages so allowing for skipping if needed, but there if you need to use them all. The activity book also has fun cut outs as well.
Would you/should I buy A and B at the same time or separate (as in 1A and 1B)?
I usually buy both together.
Did you use both A and B in one year or at all?
Because my DD was starting very young, we did K A and only a chapter or 2 of K B in one year. This year we are finishing K B and will be starting 1A probably in Sep.
Is the teacher's manual a must?
Well there isn't one for K, I bought the ones for 1st and 2nd. They have some hands on activities listed and also some things like flashcards, graph paper, dominoes that you can copy. Not a must, but it can be useful.
Do you think a child who has not done Singapore K understand the 1st grade level work if said child knows basic math (counting, basic addition and subtraction, shapes, etc)?
What you have described sounds like what is covered in the KB book. My DD is finishing subtraction right now. There is also calendar, place value, how to tell time to the hour, counting to 100, addition, money, and sequencing. If your DC knows all of that, then 1A may be a better place to start. Singapore's website does have placement tests you could print off.