Question about buying a car out of state and then titling and registering in TX (sales)

[pappy97]

Seriously thinking about buying a car out of state. May even be off eBay. As I understand it, if I do, I will send the seller certified funds, seller sends me the out of state title that has been signed over to me, and we make arrangements to get the car to me. (Probably have it shipped).

My question relates to titling and registering here:

TxDMV.GOV - Out of State and Imported Vehicles

This site says you need the following for a car you purchase out of state:

Proof of Inspection (Vehicle Inspection Report),
Proof of liability insurance meeting State of Texas minimum requirements,
The vehicle's odometer reading if it is less than 10 years old,
An original out-of-state title,
Proof of valid registration,
Proof of sales tax payment or current foreign/military ownership document,
Completed Form 130-U

My questions are on the bold

Proof of valid registration

So the seller has to send me the title and their registration on the car? That seems odd. What if I don't have their registration? Is the out of state license plate with current tags proof of valid registration?

Proof of sales tax payment or current foreign/military ownership document

Because I am buying from one state and the seller is in another state, I suspect he will not be collecting any sales tax from me for his state. If he did, sure, I'd have proof in the bill of sale. But assume I don't? Can I just say "I didn't pay any sales tax there, but I'm ready to pay TX sales/use tax?"

Thanks!!!