help, please

I am going from London to Manchester Nov 8 to see Eddie Izzard at the MEN Arena. I was hoping to check out Cardiff the next day, but...

1) How do the trains work, re: stations in Manchester? Is it simple to get from Picadilly to Victoria, for example? Should I buy my train tickets in advance or buy them at the station (I lived in London for a while but always just bought my tickets at the station) - is it really cheaper to buy online?

2) Should I hang out in Manchester much? I've never been, but I am on the market for a sparkly dress for New Year's... I like history and art, drinking and shopping, but I've got more I want to see in Cardiff, where I've also never been...

3) What's Cardiff like in terms of getting around? I'm wanting to see the bay area, Llandaff Cathedral, and poke around the city a little. I'll be going back to London that evening - is the city fairly walkable? How much are the buses, (since I know it'll be chilly)?

4) (and finally) Since I'm going London-Manchester-Cardiff-London, as well as the tubes (does Cardiff have a tube?), is there a, like, mass transit card I could buy? I don't remember how the rail passes work...

thanks

1) You can get a tram from Piccadilly to Victoria easily. Or its actually not THAT far to walk. And its through the city centre, down the main square and shopping street, so if you want to see that walking would be best.

2) Definitely hang around in Manchester if you have a chance. It has its fair share of galleries, museums, history which are definitely worth it if you've never really been before. Plus drinking and shopping would be a problem. There is an area near picadilly station with a lot of vintage and boutique shops, and a few bars worth visiting.

4) Manchester has a tram, which isn't that great (in that I live and grew up just south of the city centre, and have used it around three times in my entire life since they're only just now getting to covering any of that area), but would be very useful if you for example want to see Salford (which has the Lowry gallery, Imperial War museum and shopping etc.) and they do day passes apparently. Lots of buses, including supposedly the busiest bus route in Europe, which I can believe, from the way it crawls along.