Can I have a copy of an unique character in play if my opponent already controls a copy of the same character in play? Like if me and my opponent are both playing the Lannisters can we both marshall Sersei into play? Or can there only be one copy of any unique character in play at a time?

You can marshal your Cersei if there are no copies that you own or control already in play or in the dead pile.

But can I play my copy of an Unique character if my opponent already controls their own copy of that same character?

https://imgur.com/a/vSW20