How do I see how many of each trophy type and level I am?

[Kantor]

Alternatively,

http://www.eu.playstation.com

Update your PSN trophies (which is still manual for some reason- do what you just figured out how to do).
Then log on with your PSN details (you don't have to be in Europe), and you can see your PSN level and trophies from the comfort of Firefox!

And you can get a trophycard, and maybe people will stop calling you a Sony hater