If you have Spotify premium then yes. I've had premium for some time now so I don't know if it's changed but without premium shuffle is always toggled. So without premium you could listen to dark side of the moon, but it'd be out of order.

Shuffle? I've never encountered forced shuffle on my free account. Is this some kind of 'the mobile version is worse' thing?

Yup, for some reason you can select individual songs on the desktop client even using a free account. Not the case on mobile.

Yes. I have done this with Spotify on many car trips :)

clarifying edit: This is for the paid version of Spotify. I've never used the free version but I believe that it plays ads in between songs.