I'm not a Stumble expert, but I have been using it for a while with success. here are answers based on what I know:
1. When you give a site a thumbs up it is like a point for the site. A thumbs down is like a point against it. I think that the amount of sites you have stumbled controls how powerful your stumbles are. If you have stumbled and rated 1000 sites your thumbs up will have more influence than someone who has rated 10 sites.
2. I'm not sure how you can see the exact points, but you can get an idea what people think of a page by going to your page and then clicking the "comment on this page" balloon.
3. I don't know why you are not always shown as a person who likes a page. I know that SU watches how long you stay on a page. If you rush through stumbles and only stay for 5 seconds the value of your thumbs up may not be as high as someone that stays on a page or site for several minutes. This is probably another rating factor to combine with #1.
4. You can do searches for a specific keyword from the SU homepage. I don't know of a way to see all the sites in a category.
5. Yeah, if you want to help someone's page that you like just give it a thumbs up. If you want to do more for them you can click the comment balloon and leave a comment. You can also go the the person's SU account home page and add them as a friend and even give their profile a thumbs up. Here's my profile page:
StumbleUpon » sagegoat's web site reviews and blog
If you like the info I've given then a thumbs up to in and adding me as a friend will help me be a more powerful Stumbler.
Stumble Upon just got bought by Ebay. I expect that SU will eventually evolve into a more traditional search engine based on the thumbs up and down system. For some time folks in the Internet search industry have been predicting that search engines are going to go more social based. It's probably a good idea to get well imbedded in SU now.
I could use some stumbles and thumbs up to a new page I just created:
Baby Books