Ok, so "ig" means to make s.o. / s. th. do s. th. - My first idea was "The boy makes the dog eat." which I think is a realistic translation. That being said, I think "making someone eat" is quite different from "feeding someone". In other words: I think it's quite a stretch? What about you?
Sounds fine to me. Feeding is essentially enabling someone to eat even if not quite literally forcing them to do so (at least usually - foie gras, for example).
Note that "manĝigi" means "feed" in both sences of the English word -- you could finish this sentence "... per viando" or "...al leono" (The boy fed the dog ... with meat or ... to a lion).
So can all Esperanto words that have "ig" in it also just simply mean to enable something to do it?
Yes, you can add -ig- to pretty much anything to mean "cause ... to do ...".
Even multiple times if you want; apparently there's a book somewhere where a king says something like "Mi povas vin enkatenigigi" - I can have you put into chains. kateno = chain; enkatenigi = to cause to be in chains, to put someone into chains; enkatenigigi = to cause someone to put someone into chains. So the king can tell his servant to put the person into chains. A bit artificial, perhaps.
It's usually not "enable" but "cause".
Compare also "lerni" (to learn) and "lernigi" (to teach), though there's also "instrui".
I think you would say "la knabo farigis la hundon manĝi" if you wanted to say "the boy made the dog eat" instead of "fed." Since manĝigis is a compound, it's almost as if "manĝigi"= "to eatmake" instead of "to make eat." Like how in English "I made a snowman" means you put three snowballs together etc. etc. but "I made a snow man" sounds like you made a real man out of snow. Because it's a compound, we read it as a singular concept.
Does other languages use this make/cause to do something mutation of the verb?
What if I wanted to say The dog was fed? With the idea that chore is done. La hundo manĝiĝis? La hundo estas manĝita?
This form is allowed, but it's generally better to say "la knabo manĝigis al la hundo."
That seems odd to me if you don't say what you are feeding to the dog.
Mi ne komprenas de la bitmuzikaĵo, ĉu la knabon aŭ la hundon, ĉar ambaŭ vortoj sonas sen akuzativo
Would these be correct?
La knabo manĝigis la hundon. = The boy fed the dog. La knabo mangis la hundon. = The boy ate the dog. La knabo manĝiĝis al la hundon. = The boy was fed to the dog. La knabo manĝigis la hundon al la kato. = The boy fed the dog to the cat.