EAD based on TPS

Above is correct. Your EAD is tied to the TPS. Need to get for work authorization to be possible.

May be an issue. More facts would help. Decision will likely be more than a month.

State of massachusetts child support will not let me get passport. I pay them each month from SS check. i am in the rears.

No one has a "right" to a passport. And you won't get one if you owe too much in child support.

Can a derivative asylee obtain a green card based on family relationship of a green card holder?

Can you seek asylum for the same reason? That may be the preferred route.

How long is the process of bringing a canadian spouse to america to live and work?

Yes. Look into a different type of visa while you're still engaged. Probably best to work w/ a lawyer and get all your options laid out.

How long it takes to receive a notice for AOS interview in GA after I'll take the "Testing and Interview"from "egov-uscis.gov"?

You're still most likely several months away.

Out of status and getting married to a us citizen

Get married soon and quickly file the petition.

My I-130 has been approved recently by USCIS. And my priority date is June 2013. Catergory is F2a. Husband/Wife of LPR.

Retrogression is likely, but there's little you can do. If you're not in the US, you can only wait.

This isn't great the way you're describing it. You should get a reentry permit by filing I-131 to be on the safe side.

Related with H1b and H4

Either is possible, but your employer may make that choice for you as they control the petition.