> When I create a new ticket I can only choose states with type 'open'.
> When I create a new ticket I often want to use state with name 'waiting
> for customer' which is of type 'pending auto'.

Without any changes on your installation done, you should be able to select
pending and/or closed states.

You have to check system configuration (Agent Ticket Phone new for example)
to check if valid state types are set correctly

and second option could be ACL you should check for restrictions.