Do We have to wait for the master hearing or can we start fixing papers???

You need to retain an experienced immigration attorney immediately. If you do not, your husband will likely be deported.

I have obtained my conditions green card but my spouse is facing jail time

Unless the jail time is for spousal abuse, it should not affect your case.

Can an H1B application (first time application) get rejected because of an arrest that did not lead to a conviction (open case)?

An H-1B petition would not be rejected due to an arrest. However, if the arrest makes you deportable, it could trigger deportation...

My fiancee lives in Peru. I am about to go there to get married and apply for his immigration paperwork. how it takes?

You would file for a fiancee visa. Once your fiancee enters the US, you will have 90 days to get married. After marriage, your fiancee would need...

My boyfriend was deported a year agoandthreedaysagotheytookhimintocustudywhatwillhappendtohim

Please repost your question with proper word spacing. You are asking for free assistance, yet make it all but impossible to even read your posting....

Can an employer sponsor someone who has overstayed their student visa?

They can do their part of the process (Labor Certification, I-140), but you will not be able to do your part of the process (Adjustment of Status)...

Can L-2 continue work after L-2 visa, EAD expires and USCIS has not given any decision on the L-2 extension.

No. You must have a valid EAD at all times in order to work. Working without a valid EAD is unauthorized employment and puts you out of status.

Not enough facts. If you entered the US legally, then you can apply for the green card. If you did not enter the US legally, then you would have to...

My girlfriend is illegal in the U.S. , does she still have a chance at citizenship?.

If she entered illegally, it is highly unlikely that she can get the green card under current law. To get the green card, she would have to qualify...

I recently received voluntary departure for the US back to England, after I had overstayed my visa by 8 years,i l

You will need a waiver of the ten year bar. You must retain an experienced immigration attorney in order to have a decent chance of success.