On a new car purchase in Texas, can I deduct, in addition to sales tax paid, the other fees and taxes paid, like dealer inventory tax, documentation, title, tag fees, ..?

No, Texas does not charge tax based on the vehicle’s value. Per the IRS, you can only deduct fees that are calculated based on the vehicle's value, not the weight. You cannot deduct the documentation, inventory tax, and other items mentioned above.  

If you bought the car in Texas, but you paid car registration fees in a state that does, you may be able to get this deduction. Just enter the amount you paid on the Vehicle Registration Fees screen. 

Please be advised: You may be able to enter the amount you paid for sales tax if you are itemizing deductions. To enter the sales tax amount, please see the steps in the link below.

1. Select the Federal Taxes tab
2. Click Deductions & Credits
3. Scroll down to Estimates & Other Taxes Paid (show more)
4. Click Start next to Sales Tax
5. From here the software will walk you through adding sales tax paid for the vehicle and other sales taxes paid.

TEXAS DOES BASE IT'S VEHICLE STATE SALES TAX OFF OF THE VALUE.  As a Texas resident myself, I know this for a fact.  Per the Texas Comptroller's office:

• Sales: 6.25 percent of sales price, minus any trade-in allowance. The taxable value of private-party purchases of used motor vehicles may be based on the standard presumptive value.

Your registration, titling, doc, and all other fees are NOT deductible, but YES the state sales tax in Texas IS based on the value.

Remember that according to the IRS, on the topic of "General Sales Tax You Paid on Specified Additional Items," they state: "If the state sales tax rate on these items is higher than the general sales tax rate, include only the amount of tax you would have paid at the general sales tax rate."