When I try to play in season mode I can only choose one team. How can I choose more than one team. This is a feature that was available in all the previous fifa games. Is there a patch or something that fixes it?

Make a custom league

But if I want to play a season with league, cup and euro-cups can I do it through the custom league?

You can do it but they wont be linked, means you have to creat season and cup as two different saves. I think this is better than the linked season anyway, despite the fact injuries won't carry over between cups and leagues.

In the linked season all the goals for players are totals, not broken down between different competitions. Also suspensions for red and yellow cards carry over into European games and vice versa which is just not the way in real life.
So probably if you want some realism as far as suspensions you should make custom cups and leagues anyway.