There is no need to strain regular feed, just add more feed. If you were using whole grains then yes, because it ferments differently. Your making this more complicated and work than it needs to be.
Yes, add more feed to make it thicker. You can add a little bit more right now, if it's still to thin in the morning, just add more. The fresh in the morning won't ferment but that's fine. I still do this and I've been fermenting for a couple years.
You will be fine fermenting medicated feed. If your not using it fast enough, since you have 3 jars going, you can put it in the fridge and it will stop the fermenting process. Take it out the night before you need to use it, so it can get to room temp.
I use a crock for fermenting. I feed out...