As of the latest update to Steam, you can now PERMANENTLY remove games from your Steam account!

Steps

1. Log into Steam Support
2. Select Games, Software, etc.,
3. Select the game from the search function that shows up
4. Select the option: I want to permanently remove this game from my account.
5. Select the option: Ok, remove the listed games from my account permanently.
6. Repeat as many times as you have games you'd like to get rid of.

You can browse over your entire library and choose which software you'd like to permanently get rid of. But note, once you have removed a game from your library, it's gone permanently, so if later down the road you'd like it back you'll have to purchase it again.

You'll also need to watch out for some other issues. The thread linked above has noted that if the game is part of a bundle (HumbleBundle, etc.), removing one game from a "package" may require you to remove all the games from that specific bundle.

Unfortunately, I can't help you with how to fix the problem, but...

(Q4) Yes, yours seems to be broken. The downloads page should display the items which

• are currently being downloaded,
• would be being downloaded, but are paused (either by your action or because you're playing a game), or
• have completed downloading (these have a button to dismiss them, and also go away when you restart Steam).

(Q1) In all cases the status display at the bottom should display counts of the above 3 types of items, and a progress bar for downloads in progress. If you have a game that needs an update, then when you launch Steam it should start updating and appear in the Downloads list and summary.

(Q3) You can't cancel updates to installed games. If things are working right, you have the choice between letting the download/update finish, or doing a “Delete Local Content” (i.e. uninstall), which should cancel the download as well as deleting files. That this didn't work for you is another symptom of the problem.

(Q2) This is not normal behavior. No game should behave like this. Most likely you have some corruption in your Steam configuration which is specific to those games. For what it's worth, the usual general troubleshooting advice I've heard is “delete ClientRegistry.blob”. I get the impression this will not delete any of your settings, but I don't actually know and haven't ever done it myself.