It sounds like this is either an emergent or an expedited hearing unless service was not perfected in accordance with the court rules for petitions. A continuance most likely won't be granted but you may want to try anyway, especially if you need to obtain counsel. Mention the fact that you only received the papers a few days ago. If you receive a continuance, perhaps a pro bono legal service would represent you if you qualify for their assistance.
Instead of a continuance, a hearing will probably be held and an interim order will probably result. The court will probably schedule another hearing in the future, which could be weeks or months away.
The court will evaluate the best interest of the child in determining custody. At a minimum, you should refer to the factors described in the new custody statute to formulate your questions. Craft them to the specific facts in your case. Focus on getting the most relevant questions asked first, even if you think there are many important things you would like to get into the record if you could. This is not easy to do but since you are short on time and money, you will need to do the best you can.
PS: Please mark this as a best answer if it is most helpful to you.
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Please help me understand who you are intending to ask questions. The most important question I have is what is the issue being heard? If you have only received notice 4 days ago, my first question would be whether notice was properly served and whether you were given enough time (as prescribed by the law) to prepare for the hearing. I would also ask whether you can get an extension of time (postpone the hearing) in order to consider hiring an attorney, or at least speaking with a local attorney to prepare for your hearing. If you have limited financial means, you may consider contacting legal aid - but again, you'll need more time. In Texas, courts look at what is in the "best interest of the child" in all issues concerning child custody.