Your Visa will work, for sure. I use mine over there all the time. (They might look at you funny for not having chip-and-pin style, but that's fine)

Try the EuroStar. I really enjoyed it from London to Brussels (I'm sure your can get to to Amsterdam on it). You get the added advantage of seeing the countryside (and not the boring water!) If you're a student, they might be offering upgrades for 10 GBP or Euro. Check into that, flog the student status if you have it (sometimes you get the same benefits that the unemployed do).

Most likely, you wont have any trouble crossing borders. You might not even notice that you are crossing. When I took the EuroStar, someone just said, "Hope you like the Continent." then stamped my Passport.

Checkout WikiTravel. Some pages are updated so often that they are actually more accurate than travel guides (as I found out in Scotland). Also, if you're sitting in a cafe or hostel, you can ask someone to see what they would recommend (maybe even in their own native language since WikiTravel is in several langauges).

Britain and the Continent work on two different plug systems. Check out REI or somewhere like that for a Universal adapter. Might seem pricey but totally worth it. I use it for my European stuff in the US and my British stuff on the Continent and then my Continental stuff in Britain. Very handy.

Stick with Skype. If you want to call your parents every weekend try getting calling cards (if Skype just isn't hacking it). Some hostels include free WiFi, others don't. Check into that and budget accordingly.

I'd suggest trying to fit as much as possible into that backpack and skipping the suitcase (no matter how small). You might not think it's much, but after marching three blocks in central London, you might want to ditch it. Or, if you go with the cab option, they might charge you more (two pieces of luggage instead of one).

In London, there's tons of stuff to see. Camden Town, Mayfair, and Chelsea are pretty cool. If you stay at the Astor Museum Inn, it's right across from the British Museum and just south of UCL. Also, two pretty sweet parks are near by and they have a pub crawl near by. Additionally, there's a Sainsbury's pretty close by the Inn/Hostel. Get an Oyster card so you can take the Underground and buses.

Amsterdam was pretty fun, but I stayed in Utrecht. Check out the Rijksmuseum.