Common law marriage with ilegal alian

You have a couple of different options:
Your first option is to proceed with the divorce action.  If your husband is tied up in detention, then he may not be able to appear for a final hearing and you can get a final decree that is worded however you would like it to be.  (namely, giving your primary custody of your child and bulk of the marital estate).  In your final decree, you need to seek certain conditions which provide protection for yourself and your child, especially if you have been the victim of domestic violence.  
If your husband is out of detention and will show up to contest the divorce, then you still have options.  If you have been the victim of domestic violence, then this can serve as a basis for the judge giving you most of the community property and imposing restrictions on your husband for your protection and that of your child.  If you are in a contested divorce, I would really suggest that you obtain counsel or a legal aid attorney to help you make these arguments, since they can be a bit technical.  
Your third option is to dismiss the divorce action and gamble that your husband does not get out of detention.  Texas does recognize common law marriages.  However, if the two of you remained separated for over two years, then there is a presumption that you never intended to be married....thus negating the need for the divorce.  However, you would still eventually have to file something to get child support.  
Even if you don't need the child support right now, if you continue with the divorce, then you can get child support ordered.  It's not likely that he will ever pay it while he is deported, but if he should ever try to come back into the picture, it can be an effective tool to keep him at bay, knowing that he will be hit with a huge back child support bill.
You also ask questions about his immigration issues.  His prior marriage will not be a basis for asylum, but he can make an application to stay in the country because he has children that are still here.  His request may or may not be successful under current immigration policies.  More and more parents are getting deported despite having children who were born in the U.S.  Your question suggests that you have been a victim of domest violence.  If this is the case, you may want to let INS know so that they can take this into consideration when deciding to let him stay.  He will get one appeal....but it may proceed upward for a couple of levels.  
To protect yourself, in the meantime,  you may want to utilize the divorce action to seek a protective order or restraining order....to make sure that you and your child are safe.  
On the community property issues....the standard in Texas is "fair and equitable".  Many people assume this means 50-50....but that is not always the case.  It can be 10-90, 40-60%, or whatever the judge thinks is fair.  Judges generally strive for a 50-50, but can and will deviate if there are good reasons to do so.  Those reasons would include:  abuse by your husband, his depletion of assets, and the need for support since there is a good chance he will be deported.  There may be other reasons for deviating.  To see if there are other factors in your favor, then visit with an attorney or attend a legal clinic to visit with an attorney for additional ideas and suggestions.
If he is still detained, I strongly suggest that you get a final hearing date...and simple get a default judgment against him.  You have to provide 45 days notice of a final hearing...so the sooner you get that set, the sooner you will be able to be divorced and obtain protection.  You do not have to wait for his release to get your divorce finalized.