Do I need the original Don't Starve?

No. Don't Starve Together is a standalone purchase.

Can friends use a persistent server?

Yes. Dedicated worlds are supported; the owner supplies a Klei cluster token.

Does the PC version support controllers?

Yes. Steam lists full controller support.

Do server mods need to match?

Clients must have the content and version required by the server.

Does Don't Starve Together have multiplayer?

Yes. Don't Starve Together has multiplayer. You can have PlayBound start a dedicated server for your group and host a game on your own PC. It also supports co-op play and LAN play.

Don't Starve Together controls

No controller support

This game has no native or PlayBound-enhanced controller support yet.

Default bindings for every input method Don't Starve Together supports. These are the game's own defaults — anything you have remapped will differ.

Mouse & keyboard

Default keyboard and mouse bindings.

Every key is rebindable in the game's options.

Movement — Mouse & keyboard
Action	Default input
Move	`W, A, S, D`

Camera — Mouse & keyboard
Action	Default input
Rotate camera	`Q / E`

Combat — Mouse & keyboard
Action	Default input
Primary action / attack	`Left Mouse`

Interaction — Mouse & keyboard
Action	Default input
Inspect / secondary action	`Right Mouse`

Interface — Mouse & keyboard
Action	Default input
Map	`Tab`
Pause (singleplayer)	`P`

Multiplayer — Mouse & keyboard
Action	Default input
Open chat	`Enter`

Source: Don't Starve Wiki