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).
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.