Is there any way to get a PAL system to play in the NTSC United States?

Keeping in mind I know nothing about this particular system, I don't see why you couldn't. You should be able to find an adaptor to convert the video out on the console to one your tv will take, and assuming your tv was made in the last 10-15 years it should be able to handle both PAL and NTSC resolutions. You will probably need a step-up transformer though, but I am assuming this will be cheap as old computers aren't exactly demanding with their power consumption.

Is there a good way of playing US games on a European PS2?

(I want to buy the first Katamari)

There's some memory-card solution coming from a company called "Vast" which just plugs into the memory card slot of the PS2, and lets you boot import games on your PS2. Engadget have mentioned it a bit, and I think it's out pretty soon:

http://www.engadget.com/2007/08/24/video-of-the-vast-memory-card-ps2-modchip-working/

Other than that, I'd say one of the swap-disc soultions? I use Swap Magic.

You'll also need to ensure that you have an NTSC (or PAL-60) capable television-- an older, PAL-50-only TV will not work.

http://www.bbcmicrogames.com/GettingStarted.html

I should mention that my comment was for kv_nol, unfortunately since the BBC Micro is an old machine, it likely has no 60Hz refresh mode, so you'll be SOL without an old(ish) UK TV.

Emulation is def a better call.

I don't actually really understand what is going on u_u I think I'll need to find a conversion class thingy online for dummies.

Emulation is gay. And the UK keyboards are a bitch to work with when half the symbols don't match up.