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Yes for the first question. Slightly yes for the second. I also think girls should know how to do it.
I think the ability to repair cars and other things, and the ability to grow food, should be a graduation requirement for high school. People learn that Prince so-and-so married Princess so-and-so 800 years ago, but they haven't learned extremely basic skills like how to repair things or grow their own food.
I don't think less of a guy who doesn't, no.
But, I think having those skills can make you more appealing, or at least more of a go to guy.
Jumping a girl's car when she's stranded or offering to do particular repairs when she complains about quotes she got is actually a really good way to get her number :)
Also something like eighty percent of the time I talk about my car (only when she brings it up, cause I'm not that guy) and I mention it's a stick, it leads to her asking for a ride or to teach her or something. Yet another skill that a man can use as relationship ammunition.
I do think though there are a few basics every man needs to be aware of that I kinda tsk tsk if I see them failing at. Like how to tie a tie or which side of the car their gas cap is on.