Texas Prop. Tax; No State tax?

[Account Closed]

I've heard some stories on the Texas Prop. Tax almost being twice as much as CA. Is this indeed still true? (2.9%)

However, Texas does not have State Tax. How does this impact the higher Property Tax rate in conjunction/comparison to other states?

In CA, prop 13 has helped keep Prop. Taxes under wraps from large appreciation in home values of the past. (not so much a concern now) Is there something like this in place in Texas?

Also, what are some things that can be done, within reason, to help negate some of these expenses?

Thanks much!