apple cider vinegar--is it necessary to have the "mother" and what recipes even use this kind of vinegar?

No, the mother just kind of hangs out in the jar of some brands, but you don't need it.

I do not have any hard facts to base this on, but my guess is that apple cider vienegar is the traditional vinegar of the American kitchen. 50 years ago I do not think there was anything in the house ever but distilled white and cider vinegar with the latter used 90% of the time. Certainly other types have long histories but I think availablility at the local(non ethnic ) grocery store only happened in the last few decades. .

Not really sure what you mean. Are you wanting to make your own or are you asking if you should purchase the kind that is raw and unfiltered? I buy Braggs which is raw and contains the mother. I use it for homemade mayo, kale salad, coleslaw..lots of recipes call for AC vinegar.