Yes. Make sure you get a burr on the *entire length* of the edge on one side. When you flip the blade over on the other side, your goal is the same: Get a burr on the entire length of the other side. Only after getting a burr on BOTH sides will you know you have completely apexed the edge.
I deleted a few points in between that seemed a little confused. We come to this one which is important. The back and forth, one stroke per side, is a finishing technique to try to remove the last tiny bits of burr. But we're not there yet. At this point you should have developed a burr on one side, and then the other and right now you have a burr on that second side, full length.
So you want to remove that burr by doing a few light strokes on the stone, on the side with the burr. After every two or three strokes, feel for the burr and see if it's gone. Once it's gone it *might* form again on the other side. So check the other side too.
Once it's gone from one side maybe you feel a little on the other side, or maybe a lot. Either way, try to remove it from the other side too. But it might form on the original side again!! This is called "chasing the burr". Pulling the blade lightly through soft wood, cork, or cardboard can help strip some of this off. Once you've gotten the burr substantially reduced, it's time to do alternating strokes, one on each side, until you either feel ZERO burr on both sides, or it's as burr free as you can make it.
At this point, off of the coarse stone, it should feel very sharp, shave hair, and cut paper. If it doesn't, you probably have some burr left. Try lightly cutting soft wood, or stropping a bit. This was a revelation for me when I realized that I could shave hair with a blade straight from a coarse stone!! I've spent many, many years doing it wrong. Only when I got this did I make a leap in my sharpening. If it's not sharp, full length, off of the coarse, you're not done with that stone yet.
This isn't the right approach IMHO. I think you need to form a burr, again, on both sides with the medium stone. Only then will you know that you have apexed the edge with this new stone. Otherwise, when do you stop? You could do it visually and see the scratch pattern change to a finer pattern. But how do you know you actually hit the *edge*? You don't unless you form a burr or gain a lot of experience.
There's something else to consider here with your S30V knife. Most of the "trihone" sets have synthetic stone for the coarse, which will cut S30V. But the medium and fine are usually Arkansas stones, which pretty much *won't* cut S30V. If that's what you've got, there's almost no point in using them. Either use a different sharpening medium to get a finer edge, or just strop and be done with it. You list your stones at 600 and 1000 which sounds about like soft Arkansas and hard Arkansas. That will work (slowly) on basic stainless, but not on S30V.
Same story here as with the medium stone. Form a burr on both sides, then reduce and remove it.
Yes.
Strictly speaking, you don't have to remove the burr at each stage. But you *do* have to form a burr, on both sides, with each stone. You can leave the removal of the burr until the last stone if you want. I prefer to remove it at each stone and then test the edge with paper, hair, or both, just so I can feel the differences and so I am dead certain I've made a difference with each stone.
I hope this helped.
Brian.