This is a great third idea. I can second that these are all great, fun and cheap (or even free!) things to enjoy in Liverpool
One thing that I would like to add is that many (though not all so check ahead of time) of the Christmas carol/singing in both of the city's cathedral's are free of charge (though donations are welcome), so this is always an enjoyable and festive thing to enjoy. Check ahead on the website of both Cathedrals to see the listings!