Displaying Categorized Posts on Pages and with Calendar

I’m looking for a way to have posts of a certain category show up on a corresponding page the way they appear on my main blog page. I.E. Blog posts categorized under “Events” would show up on my “Events” page in order.

Additionally, I’m looking for a way for my future posts to show up on my events calendar on the right date.

Ideally, I would like to find a way to create a post categorized under Events, have it post regularly to the blog page, while also appearing on my events calendar as well as my events page.

I’ve searched through the plugins for days now, and have the sneaking suspicion that this might already be do-able much more easily than anything I’ve tried, but I’m out of ideas. Any help is STRONGLY appreciated.