I generally think the host is paying unless I'm told otherwise.

I don't mind being told I'm paying for my meal though! That's fine. So long as I know and have a vague idea of costs. I generally take some cash with me for drinks etc and know where the nearest cashpoint is - DH or I can dash to it and leave the other one in the restaurant!

The card could say:
Come celebrate X's birthday! We're celebrating at Y restaurant on the 19th of August at 7.00pm (for eg). We have enclosed a menu with prices on for your information. Please bring a bit extra if you would like drinks.

Love,
Me.