Playing with others

Can it be played with random people and if so how? Or is just only friends?

You can search for random games using LB, however it is a little weird how they do it.

If you want to find an arcade game you will need to select arcade mode and the difficulty, at the character select screen you can press LB to find other games. It will also tell you the % through the arcade mode that person has progressed.

For jumping into another persons story mode you will need to be on the episode in question, so when you first start and are on episode 1 you will only be able to look for games that are also on episode 1

Going to the map and moving to a different episode allows you to search for games on those episodes, you can obviously only move to episodes you have already unlocked in your game on the map though.
Essentially making sure you don't skip all the way to the end of the story mode using someone else's game (there is a way around that though, but takes a bit of luck)

Probably doesn't make sense but if you are in the game it should be clearer

To make it a bit more complicated…

Even though you select a difficulty for Arcade mode, this is just for your local game. It doesn’t actually filter lobbies by that difficulty. There is actually no way to tell from the lobby what difficulty it is. You have to jump into the game to find out.

A tip though: start with 5 lives=easy, 3 lives and regular damage=Normal, 3 lives and double damage=hard.