I just caught an Abra with Teleport and wanted to go back to a Pokémon Center. I have my Pokémon selection screen open, but it doesn't seem like I can use Teleport outside of battle. Am I still able to do that, or has that feature been removed? I would imagine this applies to things like Sweet Scent and HMs like Surf.
I don't think you will find HMs in Sun and Moon. Surf, Fly and Waterfall used to be HMs but now they should only be relegated to TMs.
In Sun and Moon there's a new feature Poké Ride that allows you to ride on certain Pokémon. Each Pokémon allows the player to use a special ability.
Lapras Paddle allows the player to to surf across water. The player can also fish from Lapras's back.
Sharpedo Jet allows the player to surf rapidly and smash through rocks in the water.
Regarding Teleport, the SunMoon description only states:
Use it to flee from any wild Pokémon.
when in XY and ORAS it was:
Use it to flee from any wild Pokémon. It can also warp to the last Pokémon Center visited.
so it seems that it doesn't work anymore.
The same for Sweet Scent, its description only states
A sweet scent that harshly lowers opposing Pokémon’s evasiveness.
without any reference about if it can be used outside of battle.