Some questions, for newb, on property tax foreclosures in Texas, Fort Bend County

[Roger Malcolm]

I have never bought a foreclosed property. There is one near me that I am watching.  Some questions please:

1) How long does it take a property to go to auction, once the property tax are delinquent past July?  July is the month when the penalties go up the most due to accruing the legal cost of foreclosing as I understand it.  So now that the first July, since being not paying taxes has hit, I am wondering if it is still far off, or now is right around the corner.

2) If you buy a property at a property tax foreclosure, and the prior owner buys it back in the two year period, would you only get your money and premium set by law, or would the prior owner also have to pay for the property taxes you paid during that period?  What about improvements?   I.e., would you lose all that or you get paid for those?

Thanks for helping me with either of these.