Many of these words mean the same thing or, at least, cross over into each others territory. But just like English some of these are used in certain contexts that just can't be defined in strict language rules. Like in English you can say something is "very funny" but saying something is "very fun" sounds weird. "A lot of fun" is more natural, but "a lot of funny" is never said. These sort of rules you just have to pick up with experience.
"This is very fun" not accepted as of 9/12/17, although one translation of 재미있음 is "to be fun."
Also, why not substitute 매우 with 정말? In this context, they mean the same thing.
I dont have a lot of experience with 매우 specitically, so I'm unaware of any nuance difference, but regardless learning synonyms is important in any language.
Quite confused about 매우, 아주, 너무, 많이, etc. Are they interchangeable or do the context matter for each word?
I struggle with this too. I do know that many of these can vary. Here is my limited understanding: 너무 also has the meaning of too much or in excess. 정말 and 진짜 both mean really. 많이 means a lot. I believe 아주 is closer to 'completely' but isn't as common in spoken Korean, it's more of a written phrase. Don't get discouraged though! English has a lot of these types of words as well. Really, extremely, excessivly, too, super, etc. I would just try to pay attention when you hear them used and you'll get used to when to use each - or so I'm told :)
don't take my word for this because I'm not a native speaker, but i noticed that people use 진짜 a lot as an exclamation but they don't really use 정말 in that way
They are not interchangeable. The first two 매우, and 아주 can indicate varying degrees of "a lot". 너무 literally means "too much" and only means "very" in colloquial usage. 많이 literally means "many times" and shouldn't really be used to indicate "very". They may translate to similar definitions, but they have subtle differences between them.
Why isn't extremely interesting accepted? 매우 translates literally to extremely.