Change custody start time due to new job?

You really should speak to an attorney regarding your issue. Additionally, based on what I am seeing here, it is possible that the Court is saying...

Can one parent deny access to the child to another parent; non-immigrant family?

You need to file some sort of petition for custody. Please speak to counsel for more advice.

Possibly. You would need to serve him with the paperwork properly, and then prove your case in court. Please hire counsel for this work. Its not an...

You can but I really would not recommend it. I would strongly suggest you speak to an attorney for guidance.

I was granted sole legal and physical custody of my 5 year old daughter on 5/23/2017 I Inform the father to explain we are going

Its unclear as to what you are asking. Please provide more information.

Please get an attorney. Please do not make a mistake and proceed pro se.

Can I get custody of my step children when their father wants me to keep them?

As counsel said, unless you adopt them, you lack standing.

What are the chances my fiancé will be able to adopt my 2 kids?

If the father does not consent, it will be really really difficult to terminate his parental rights.

Can I Move My Kids Too New York State With Me ?

If you move, you need to get court permission, unless you want to risk getting hauled back to florida with the kids.

Can I apply for food stamps, medicaid, and childcare for my grandchildren in NY?

You should ask social services if you can.