Can people stop downvoting people that are genuinely just asking questions please? It's not cool and makes me sad whenever I see it. Some people on this site may not be English natives and even if they are, it's not on to mock someone for asking a question, how are people meant to learn otherwise..?
Native speaker here: No, there is no pain implied any more than there is in the English "hurry".
Looking at Wiktionary myself, the German "schänden" seems to be derived from the similar word "skandijaną", not from "skundijaną". Swedish does have an equivalent to "schänden" though in the word "skända", which means "defile" or "bring dishonour upon". Just like the English "defile", it can be used both for defiling graves and as a less brazen way of referring to rape.
Now this post is old but anyway. If you trust wiktionary, it derives from proto-germanic: "skundijaną" (to accelerate) and is related to German "schänden" and Dutch "schenden" which both mean "to violate", "to defile", "to rape" etc.
I guess it's very likely that schinden has the same root.
I can only think of one instance where "we hurry ourselves home" would be used. In the southern U.S., the reflexive is emphasized in a more or less sarcastic reply to a request viewed as wildly unimportant. "Bless your heart. We'll just hurry our (little) selves back home to get your lunch."
No, because äter is not a reflexive verb like skyndar is, so it requires the reflexive pronoun, just like har på sig (taught in the clothing section). The tips for this section explains more about reflexive verbs and even uses skyndar as an example. https://www.duolingo.com/skill/sv/Verbs%3A-Present-3/tips-and-notes