Can you see if a game has trading card support on its 'Library Page'?

Right now on the Featured Items page of the store if a game has Card support it has a sash over the top left corner that says 'Cards'. On your profile, the badges section is a list of all your games that have badge/card support.

But at the moment I don't see anything on the game Library page in any of the 3 views (Detail, List, or Grid) that has any indication of card/badge support.

Is there an individual marker in any Library view (similar to the Cloud in List view that shows Steam Cloud support) to see if a game has trading card support?

No, you cannot see if a game has Trading Card support from its Library page. If you want to see which of your games support Steam Trading cards, use the Badges section of your Profile that you mentioned. If you want to check a specific game you own, you're gonna have to look it up there, or just search around a bit.