If you can, feel the texture and stretch the material between your fingers. It is common for more stretch one way than the other.
That depends. Some vinyl only stretches 2 ways, while others stretch 4 ways. (like Morbern Allsport) You need to check the spec sheet on the vinyl. A door panel should not give you that many headaches, just buy a good grade of vinyl, not $2.00 a yard at some closeout store. Another choice is marine vinyl which is more UV resistant and resists oil, gas, and mildew. Go to an upholstery shop and ask. They will show you the spec sheets, help you choose, and answer all your questions.
Ultraleather is not vinyl, it is 100% polyurethane, not PVC like Naugahyde,( a name brand used generically in referring to vinyl) Ultraleather stretches a lot. It is also 2 to 3 times the price of vinyl.
The benchmark for all fabric, including vinyl and ultraleather, is the Wyzenbeek test.(also on all fabric spec sheets) This is a test that abrades the fabric by rubbing it forward and back. The more double rubs the fabric can withstand, the better the fabric. Ultraleather will win that contest hands down, but how much punishment like that is a door panel going to get?