Can one assume that like English "wheels" is an idiom for car, or is it more general?
It's not an idiom for car, it just means wheels. It may be what you would say, for example, if someone expected you to arrive too quickly from one place to another: well excuse me, I don't have wheels! Or something like that.
... or when they try to slide you along the floor. "Stop that. I don't have wheels!"
lרגליים. But, if you really want to specify the feet, not legs, you would have to use כַּף הָרֶגֶל. And the plural would presumably be כפות, but maybe someone could confirm that. Hebrew is one of those languages that doesn't have a special word for 'foot'. Instead, it uses an expression that literally means 'the spoon of the leg', or 'the sole of the leg', for foot. In daily life, however, everyone just says רגליים.
Well, the plural of כַּף in the sense of spoon is כַּפּוֹת, but for palms כַּפַּ֫יִם. But because the language avoids a construct chain of two duals (already visible in 1S 5.4 ושתי כפות ידיו where the numeral two is added to clarify), the expression כַּפּוֹת-רַגְלַ֫יִם is used. I think palm is the older meaning, but to use the word for palm-like instruments is an old usage (Ex 25.29 ועשית קערתיו וכפתיו וקשותיו ומנקיתיו אשר יסך בהן "And thou shalt make the dishes thereof, and the spoons thereof, and the flagons thereof, and the bowls thereof, wherewith to pour out:").
Very interesing, IngebordHa14! How common are double possessives? In what context are they used and in what social register?
Well, I think it is used as an intensifier, like בְּנִי שֶׁלִּי my own son or יָדַי שֶׁלִּי my own hands. I guess it is often used with members of your family and your body, but maybe there are other occurrences too. As always with the possessive suffixes, the register is higher, but for the cited words they are still usually used.
Wheels and tires are synonymous in English. So why can't it translate that way... I don't have tires.
The tires are the rubber things. The wheels are the metal things on which those tires get mounted. Have learned this the hard way... NYC potholes. I've punctured tires and I've bent wheels. Granted, people refer to their cars as "their wheels". But that's just an expression.