How does the Time Traveller know what the Morlocks are called if he doesn't understand their language and the Eloi don't acknowledge their existence?
He mentions that he picked up a few words of the Eloi language, so presumably he finally got one of them - probably Weena - to make a direct reference to the hairy underground flesh-eaters and picked up that that was the word for them
When he finally gets the machine back, why does the Time Traveller go forward all those millions of years before going home, when he'd made it clear several times he was desperate to get back?
Curiosity killed the cat?
That's answered in the book: he was frantically grabbing at the controls while trying to escape the Morlocks, and didn't realise until after he was in flight that he'd pushed the lever the wrong way.
Why, upon his return, does the traveller so adamantly demand meat? You'd think he'd be turned off of it for a while after what he learned about his futuristic friends...
Probably he wanted to eat something familiar to help him cope with the stress of the trip.