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"wouldn't it reduce the likelihood of drawing one that's contextually useful...?" -- YES!

Killing chickens for their runes is voluntary (unless they are blocking your path). And you can see their color ahead of time so you know what color rune you will get. But understand that the game is incomplete. There are some mechanics that I intended to have that I just didn't get to. I am continuing to work on the game though, and hopefully will solve some of these problems.
To answer some questions:

For onboarding, all I had time for was tooltips :(

Order doesn't matter.

You can only lose health from walking into chickens or when then enemy takes a turn in combat -- nothing spontaneous. 

It is meant to be like poker and Yahtzee -- there is some overlap there. You can lock runes and redraw once per turn somewhat like Yahtzee or draw poker.

Mana is only used for your lightning spell to kill chickens. It's not well balanced currently.

There are a few sad bits. I accidentally left the last boss with 1 health. There is no way out of the dungeon. You can go to lower floors but they are empty. My next version, after the competition closes will resolve these issues.

One of the big pieces that didn't make it in, is that you will eventually be able to play up to 3 runecards at a time. You will redraw runes each time you play 5 runestones, but if you have to play an empty runecard, it will damage you, like the spell blowing up in your face. Runecards will have properties on them that are more interesting than All mana x2 and All damage x2. I envision wild runes, cursed runes and ways to prune your collection. You'll eventually do millions of damage and be rewarded for overkills. You'll also face monsters with millions of health.

Thanks for playing and thanks for the feedback!

After watching your videos, I do see some bugs, and one of them looks like the spontaneous damage you mention. The monsters healing is a bug. You taking damage from your own turn is a bug.