Do interfaces in PHP have properties, or do they only have methods?
It depends what you mean by "properties". If you mean actual fields, then no, they don't. If you're referring to properties such as those in C#, then yes they can (since the property accessors are strictly syntactic sugar for accessor methods anyway). The same goes for events (though of course, in each case, no implementation is specified for the get/set or add/remove accessors).
Update: Since PHP does not have properties in the sense of get/set accessors, then the answer to your question is no. Interfaces cannot carry their own data/state.