I bought a table saw recently and it's the most terrifying tool I own.
As a beginner, that is the right attitude. I note that the most dangerous time will be when you are no longer a beginner but not yet an expert; that's when people make careless mistakes. I try to remind myself frequently that my table saw is trying to kill me.
It doesn't feel good to use the fence, one at a time, because it's difficult to keep the board flush to it given only 5" contacts the fence with 14" distance to the blade.
Correct. This is a recipe for the work rotating and kicking back.
And you never want to use the miter slide and fence in combination because again, the work can bind against the fence and rotate away from the miter. However there is a way to safely use the fence as a reference; more on that in a minute.
I could use the mitre slide but I'm not sure how to get consistent position for multiple cuts. Is there some magic jig I can cut or a good marking / measuring technique for the mitre slide? (I am thinking, maybe I can make an "L", laying on its side, with the long edge mounted to the slide and the short edge 14" from the blade, but I foresee problems keeping the angles true and the short edge sturdy; I could make it out of scrap steel maybe but now it seems like a whole project of its own.)
If you're going to go to that kind of trouble then it is better as others have noted to simply make a sled. I use my sled for all but the most trivial cross cuts.
Can I somehow load all the boards at once? I was thinking maybe I could temporarily mount them all to a piece of plywood or something then run the whole thing along the fence, maybe once to make all the edges flush then flip it around to cut the dados. But I don't want to put screw or brad holes in the boards and I'm not sure how to mount them otherwise.
Not worth it. It'll be hard to keep everything together and awkward to try to cut so much at once. And this is not the last time you will have to solve this problem.
How can I safely and accurately make these cuts?
The cheap solution is to use the fence as a reference but not keep the work against the fence while it is being cut. You reference the fence before the work engages the blade like this: (Though I personally would be inclined to use the other miter slot.)
Clamp a scrap known-to-be-flat board to the start of the fence, set the fence-with-board as your reference, and push the work against the board before you start moving the miter. When the work engages the blade it is past the board, and so there is no chance that the fence will bind against the work.
But again, building a sled pays big dividends. Repeatable, accurate cuts are easier, and you can build as many safety devices into a sled as you desire. My sled is covered with points where clamps can be added to hold work in place. Hands are terrible clamps.