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
Worth noting that the Time Traveller at several points admits that he's got no real certainty of whether or not his many speculations and hypotheses about the future society are actually accurate, but is just drawing the best conclusions he can based on his observations. Presumably he can't be 100% certain that the name he's associated with the Morlocks and the Eloi is actually the correct name that they actually are identified or identify themselves with, but is simply calling them both that because (a) he's heard those words/noises used around them and is assuming they apply, (b) he needs to call them something for purposes of clarity and conciseness, and (c) it's not like either his audience or the entities in question are in a position to challenge or correct him anyway.
Or alternatively: we've got a bit of Unreliable Narrator going on, the Time Traveller doesn't actually know what they're really called, and is just giving both groups a name which to him seems appropriate. Since, as mentioned above, it's not like anyone can challenge him on it anyway.
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.
To quote Professor Arturo from Sliders, "my stomach has no political preferences." The Time Traveller clearly isn't a vegetarian yet routine, and so is used to having meat in his diet. He has also subsisted for a week (from his perspective) on nothing but fruit. He's probably starving for the taste of meat. Also, his exact words indicate at the time would seem to suggest that the food he's survived on so far hasn't given him much in the way of protein, and meat is probably the closest thing available to fill that particular need. Plus, to be fair to him, him chowing down on a bit of mutton isn't exactly the same as the Morlocks resorting to cannibalism, since it's a different speciesnote And if we want to be technical, the Morlocks have arguably evolved into a different species that the Eloi anyway, albeit both species being derived from humanity. Presumably the Time Traveller simply has a strong stomach / constitution.
What do the Morlocks eat, other than Eloi? It seems unlikely that the Eloi are numerous enough to be their sole food source.
They might also eat some of that fruit that the Eloi are fond of eating. Besides which, we don't know if the Time Traveller has visited the only 'pen' that the Morlocks keep Eloi farmed in; they could be all over the place. It's a big world, and really the Time Traveller only sees a small corner of it.