" If my mmr is higher than average for that division, will I gain more lp for winning, less for losing, "
No, but having high mmr than average for your vision can lead you to get matched in games where you gain more LP than average for winning and lose less LP for losing. Your LP gain/loss depends on the average elo of the players you get matched with in your current game so having better than average mmr helps you get those types of games. Sometimes, loss prevention may be turned on which means if you lose, you dont lose any LP but you DO lose MMR and if you win, you gain less MMR than usual.
"and get paired with less-skilled people?"
There are "less-skilled" players at every elo. If they're playing below the skill level of the other players in their elo, they may be considered "less-skilled" by some of these players. Besides, you shouldn't be focused on another player's performance. Instead, focus on trying to win the game.