It sounds like Hungarian effectively built this into the language, which is super interesting!
Because it really affects the meaning, I also think that your parent's statement that "you typically rearrange the sentence to emphasize the important part" is not strong enough. You don't just "typically" do this. You do it because you must, because most permutations of a given set of words -- although perfectly grammatical, and referring to the same event -- are simply pragmatically incorrect in the context of the conversation or text.
Absolutely. So much so that in the Hungarian dub of Star Wars Yoda speaks normaly, like any other character. His vocal weirdness thing completely gets lost in the translation.
Yes. My point was merely that this is bad. Yoda is supposed to talk differently. If he doesn't, then the translator didn't do their job properly.
Not exactly irrelevant, but very flexible. There are some rules to word order in Hungarian, but you typically rearrange the sentence to emphasize the important part by putting whatever is important in front. For example, if you ask a question, the question word that you expect an answer to always goes in front, "What should I wear?" and the answer should start with the word that answers that question, "The red dress, you should wear". Without delving into an entire Hungarian grammar lesson [because 1) I'm not qualified and 2) It would take several months], you can think of word order in Hungarian like the word order that Yoda uses. Yoda might say "Patience you must have my young Padawan." but he would never say "Must have you young Padawan patience." Why? Because he's putting emphasis on patience, so he starts the sentence with that, and then the rest of the sentence falls into an order behind that, but isn't random.
Also, while Finnish and Hungarian both have flexible word order and are both agglutinative, a language being agglutinative has little to do with word order and is about the fact that rather than using multiple words, you add prefixes and suffixes to words to add meaning. For example, "I play with my dog" is only two "words" in Hungarian: "kutyámmal játszom" which is basically "dog+my+with play+i", but because of the agglutinative nature, the boundary between what is a "word" and what is a sentence is a bit fuzzy and the words can get very long, for example: "megszentségteleníthetetlenségeskedéseitekért" which roughly translates to "because of y'all's continued behavior as if you could not be desecrated".
Because of agglutination Hungarian also has a very fun tongue twister: "Te tetted e tettetett tettet? Te tettetett tettek tettese, te!" which basically means, "Did you do this pretend deed? You doer of pretend deeds, you!"