What do I have to put under my pillow to get the weiner fairy to visit in the night?
I keep wondering....
Why do folks in the US so often spell 'Wieners' as 'Weiners'?
Isn't it because weiners are named for the city of Wein (like hamburger for the city of Hamburg or frankfurter for the city of Frankfurt)? Weiner would seem to be the correct spelling?

They are (loosely) named for Wien (aka Vienna) in Austria. In German, the ie/ei diphthongs are said as the second letter. Wien is "veen", Wein is "vine" (wine). Wiener is the short form of Wienerwurst (Viennese Sausage).

Americans run into plenty of German/Yiddish names, e.g.
Dianne Feinstein, Albert Einstein (correctly, for English, following the German form) FINE-STINE INE-STINE,
Harvey Weinstein & Harvey Firestein (oddly, mixed) WINE-STEEN, FIRE-STEEN
Epstein (EpSTINE or EpSTEEN - as in Epstein-Barr Syndrome)
and most people have no way to know which is which nor do they much care.

The folk reasoning for this is: "When two vowels go walking, the first one does the talking." Which is the opposite of German/Yiddish, where (for EI/IE) the second one is the one we say/hear.
"No Skins"... so, that would be "cut" in the Craigslist ad, right?
I am trying to imagine a skinless frank? Like bologna with the casing removed? I think the skin is actually a GOOD thing?
Actually, any hot dog you buy nowadays is skinless. The casing or skin is removed after they're cooked at the factory. It's really just used to keep things from falling apart until they're cooked.

If you ever see video of hot dogs being made, you'll notice that for much of the process they have a black stripe running the length of 'em. That's the casing.

Even most bologna is sold 'skinless.' You can find some brands that'll have what looks like plastic around each slice. That'd be the casing left on instead of having been removed. In the case of meats like bologna, the skin often has brand logos and stuff printed on it.
The fact that Granny there in that first ad looks like a dude in drag makes this ad more disturbing to me. Don't get me wrong - I love me some queens, but Granny/Grandpappy there isn't even trying!
In the second ad, I'm just glad Jean and the other adults sent the children away before they got too far into their wiener-a-trois.
It's hard to hear/read the word "wieners" and not snicker like a 12 year old. ;D