You have a lawyer representing you, and that lawyer is working closely with the prosecutor. These questions should be directed to your lawyer who is in the best position to provide advice to you.
Generally when a case is reduced from one charge to another, it comes up in a manner that confuses most people. It will show the original charge, and of course it is in a felony court. If the person checking the background checks further, they will find the notations that the case was reduced to the misdemeanor charge. Unfortunately, many agencies who conduct background checks do not go this far, or do not care.
On the question of whether you can have the case sealed, I am not sure. Is it an assault family violence? Anyway, you know that nondisclosure is not a matter of right - it is a matter of discretion with the judge in your court. I have nothing specific to base this on but I highly doubt that a Harris County felony judge (or at least about 19 of the 22) would even consider nondisclosure on a charge that was originally aggravated sexual assault of a child. And if they would not, then there is nothing that you can do about it.
Yes, it is possible for the ADA to refile the case altogether. This might give you more leeway in getting it off your record vis-a-vis expunction but even then I believe that Harris County would probably fight the expunction (but at least the case would show "dismissed".)
These are good questions and important to your decision on whether to plead or take a chance in trial. (It certainly raises a huge red flag that the State is willing to reduce this type of charge to a misdemeanor assault. They obviously have some major issues with their proof.) However, these questions are better answered by your lawyer.
Although I have answered the question to try to help you, you should consult with a lawyer in your area in person on the matter. In addition, my answer does not establish an attorney-client relationship between us.
You absolutely need a good criminal defense lawyer to assist you in this case. In most states, even if you are convicted of a lesser offense you become a registered sex offender. Do not do anything until you have consulted with a lawyer working for you on the case.
This response does not create an attorney client relationship and is offered for informational purposes only. Only a lawyer fully versed on the facts and circumstances of your case can properly advise you on the case. I am licensed to practice in Minnesota, not every state. You should always consult with an attorney licensed in your area on how best to proceed.
A reduction from a First Degree Agg Sex Assault case to a Class A Misdemeanor Assault certainly seems like a good deal on its face, but if you aren't guilty, no "deal" is a good one. By pleading guilty to anything, you won't be eligible for an expunction. If your plea on the assault case includes an affirmative finding of domestic violence, you won't be eligible for a Petition for Non-Disclosure, either. In other words, you won't be able to seal it.
A D.A. can refile a case at any time, provided the statute of limitations have not run and jeopardy hasn't attached. If you plead on the assault as a "lesser offense", I think that would most likely constitute jeopardy having attached and would be a ban on them refiling, however.