I want to whether I am eligible for cap exemption?

Are you still in H1b status? If you return as an H1b, you can. If not, it seems to me that you cannot.

I don't know when to apply for a green card

You should wait for a decision from the Board and then file.

I'm getting married to a U.S. Citizen and will be changing my name. Can I use this new name to apply for a status adjustment?

Yes.

Can my mother get a travel document/extension for the third time?

There is no law against it, but it is evident that she risks abandoning her residence in the U.S.

How long do they give you a visa for after I-30 has been filed prior to get a greencard?

I have seen as short as 30 days and as long as 90 days. Once they arrive, they will get stamps in their passports indicating they are permanent...

My boyfriend is in jail he served his time now he is going to immagration can he get out with bail

No, if there is an ICE hold, ICE will detain him. You need to pay the bond to the traffic court in order to start this process, though.

I got a RFE for my pending 1-485. Should I be worried?

Until you know what it says, there is no way to know if you should be worried or not.

You could file an application for replacement citizenship application. Also, to file for your daughter, your US passport will also suffice.

I have posted bond twice through ICE, one in 2009 and one in 2013, can I get the original bond I posted (2009) returned?

No, if your removal proceedings are not over they bond cannot yet be returned.

Do I need to use an immigration attorney to apply for permanent residency?

A lawyer can certainly help make sure the forms are completed correctly, the supporting documentation is included, and is adequate, and to prepare...