Not sure if Texas is the best state or not, but here are a few ideas.
There's not really much of a struck off list in most places.
Every county handles this a bit differently. Some allow you to bid immediately after the sale....some don't allow that...some put them in the auction again in the future one or two times, before they really hit the struck off list that you could bid on. I think there are a few places that hold them for a couple years to get rid of the redemption /contest issue and then resale them either at auction or on the struck off list.
So you want to know what is the situation, before you immediately begin fixing the house. You want to know what the redemption period is, if any before you start fixing. If for some chance there is a redemption or contest of the sale, you are only limited to recovery of your purchase price plus the penalty and repairs that were due are safety, security, or preservation of the property. For example if you had a bad roof, you might be able to put on a new roof to preserve the integrity of the property, but you might not be reimbursed for paint, tile, carpet if it was not needed..to protect the safety or security of the property.
Redemption are probably rare....but they do happen. I have one going on right now.
Some say the redemption period is 6months, but I think in reality is 2 years. Redemption period starts once the deed is filed with the county in your name in most cases. As mentioned above sometimes the taxing entity will strike off in their name and then not resell it until the redemption period is over and then if you buy there would be no redemption period.
You are correct about not getting straight answers. That is because most of the time you won't talk to anyone who really knows...and often the people you talk to at the law firms are not attorney's or even paralegals..sometimes they're just office staff. Not a slight at all...some know plenty and share plenty, but not always. Sometimes the taxing entities don't know. I called one county this month about the December sale and the only person in the office said there was no sale. I pushed and pushed and then she said the Tax Assessor is out until 12/3 so they couldn't have a sale on 12/4. Finally was able to confirm there is a sale.
So after you buy at the sale or even after the sale it may be anywhere from a couple of days to maybe 4 months before the deed is filed. Normally about 30 days in my experience, but had one last month filed same week, and another one last year took about 4 months or maybe longer. So the time period, either 180 days or 2 years doesn't start running until the deed gets filed. Working on one now that has taken about 3 months to get the deed.
What counts.....well you have to think of what a judge or jury might find in a court of law. I probably would not want to test these theories for fear the decider wouldn't agree. Every expert I know says don't rehab them....change the locks, fix the leaks, repair the broken windows, but don't replace the carpet, the countertops, etc. They often tell you that at the sale is well. If it is a vacant lot, don't build a house...until the redemption period is up....I'd say until 2years is up.
Be aware it is not only the owner that can redeem, but someone who purchases their rights. There are plenty of people watching...you make the house really nice, maybe we hunt down the prior owner, give them $1000 for the redemption rights and buy the house back from you. Believe me...there are people watching.