Texas Property Tax assessment and projection

[David Andrzejek]

I'm an investor from California, looking at a property in Texas... familiar with CA tax but not TX tax.  I've done some searching on the web and on BP and not quite getting to my answer so hoping someone knowledgeable can help while I continue to search/read. 

I'm looking at a MF in Austin. From owner-supplied financial records, best I can tell owner paid ~55k in property tax last year, close to county records of 58k bill (owner records are messy so I likely missed something).  From appraisal statement, last year's assessed value was 2.661M.  Since then, property was bought by an agent, who is offering it for sale.  This year's assessment is 3.21M, which would mean prop tax bill of 70.5k at the local rate.  

At asking price, tax would go to 120k, IF the property was assessed at current asking price (ie if I pay asking, and if assessment is based on that sales price).  Agent has claimed they are a) protesting the current assessment and b) taxes only go up over time  (in conflict with my factoring immediate sales-price assessment into my business plan to work back to offer price).

Question:

1) How are property values assessed? is recent sale values used (like in CA). I've read other posts here that TX is 'no disclosure' but would be great to hear from TX investor how this actually works. 

2) is there any cap on increases, or can value jump from 2019 to 2020? 

How much the prop tax is and how it is assessed over time makes a big difference in the attractiveness of this deal (go/no-go) so I need to understand how this works. Obviously i'm not taking agent/seller's POV... need to know myself.  Deal fits my target profile so far but as everyone here knows numbers *have* to work! :)