What if I don't remove the jam token? What does being Jammed actually do? Who decides to remove the jam token? After all removing the token has an adverse effect but what does having it do?

The token removes itself to devour the next focus/evade/etc you get. You don't have a choice.

I believe they choose if they have multiple already when you jam them.

Having it means you are jammed.

Which in and of itself does nothing. Except that some game elements trigger off Jammed targets. Ferophs ability and the jam action itself among others.