Looking to buy a house for 200K but.....

Okay guys I’m gonna use this to spring board into the answers I’ve always wanted to know, so here goes....

-I’m engaged with an infant child

-I work in law enforcement and make about 100K

-fiancé works for a hospital and makes about 31K

I have a credit score of 710 and have about 6K in debt (50-150$ minimum payments)

We really want a house in the westchester county area and hoping to get approved for a 200K loan for a small starter home, we only wanna put 3.5%

We qualify for all the First time home buyer programs, my questions are

1) is it possible?

2) what are property taxes? When and how are they paid?

3) can I come out of this with only the 3.5% out of pocket (not including inspections, etc)

4) can I put closing costs into my mortgage?

5) working with a mortgage broker to save me leg work considering my schedule, do you recommend?

6) assuming all the stars line up perfectly, how long before you can actually move in and close?