Are people who Kelemvor sticks in The Wall there for good? Is this specifically and unambiguously told to the clergy? Is there room for schools of thought on the topic that make Kelemvor seem like less of a bastard, like if they fully accept Kelemvor's rule and vow to serve him he'll let them meander around the Fugue and escort the dead around (or something).

Not being able to move and interact with others while remaining conscious would be a terrible way to spend an infinite amount of time, and punishing temporary mortal failings of a limited duration with an infinity of punishment seems like an extremely unjust punishment for a deity who's reputed to be a fair judge.

I -think- only the faithless go to the wall, and Kelemvor's priests and such go to the City of Dead like everyone else.

However, Kelemvor's been completely changed by WotC so many times that I could be completely wrong and someone who owns 500 source books should feel free to correct me!

No God = Go to the wall of the faithless for eternity

Patron Deity = Your soul is property of your god. He can come and collect you whenever he wants. This goes for servants of Kelemvor too.

This is not a system Kelemvor created, I'm pretty sure. It is all the dictate of Ao. Kelemvor is just the gatekeeper. He didn't set these very harsh rules, he only enforces them to the best of his ability.

But are these rules clearly explained to mortals? Is it an unchangeable law that everyone accepts, like gravity, or is it more abstract, like the concepts or rules in RL religions, which would leave room to gloss this over?

It is factual, and a cleric, especially of Kelemvor, would likely know about the false/faithless/faithful.

Everyone knows faithless go to something not nice. Whether they realize they are stuck in a wall or not is disputable.