Types of things you could write to them about include introductions, invitations to premieres/plays; you could be thanking them for some advice they gave you, you could have seen something they are casting for and would like to request an audition, or it could be something else entirely- use your imagination.
Can I wear jeans to an audition?
You don’t need to dress like you’re going in for a corporate interview here. Your clothes shouldn’t be a wrinkled mess, but you also shouldn’t be wearing business attire to an audition. A good pair of jeans can go a long way, and it’s worth investing in a pair for auditions alone.