Tank 3 should be fine for Jackson and he will indeed keeping the bacteria ticking along for a hospital tank. (Normally in a hospital tank situation, you only have one or two fish going in there, so there shouldn't be an issue there at all - now or in the future.)
Tank 2 is coming along. I see the drop in nitrites, and the drop in pH. Those items being linked is a good sign. Decrease in nitrite should be accompanied by an increase in nitrates, and even though your test didn't show it, your pH dropped, which would be another sign of a nitrate rise. It's going to happen. It's just going to take a bit more patience, I'm afraid. But, on the positive side, you have two tanks with fish and they are both showing double zeros!
You are getting close to the point where you could steal a little media from Tank 1 to seed Tank 2 a little more. (You did say that you had ceramics, right? If so, just grab a small handful and place them into the filter of Tank 2 (I usually keep mine in an empty filter floss "bag" - it makes is easier to "clean"). That would give your cycle there a little boost, without harming Tank 1. Just replace the amount of ceramics you move over and it will be colonized in no time.
I would also mention that the movement of ceramics like this will also help Tank 3, in the case that you need to add more than just one or two fish to that tank in the future. Just grab a handful of ceramics from whichever tank has the most fish in it at the time and replace. Tank 3 will be good to go almost instantly.
Are you keeping up with your water changes on Tank 3 so that Jackson has clean water to heal in?
Tank 2 is coming along. I see the drop in nitrites, and the drop in pH. Those items being linked is a good sign. Decrease in nitrite should be accompanied by an increase in nitrates, and even though your test didn't show it, your pH dropped, which would be another sign of a nitrate rise. It's going to happen. It's just going to take a bit more patience, I'm afraid. But, on the positive side, you have two tanks with fish and they are both showing double zeros!
You are getting close to the point where you could steal a little media from Tank 1 to seed Tank 2 a little more. (You did say that you had ceramics, right? If so, just grab a small handful and place them into the filter of Tank 2 (I usually keep mine in an empty filter floss "bag" - it makes is easier to "clean"). That would give your cycle there a little boost, without harming Tank 1. Just replace the amount of ceramics you move over and it will be colonized in no time.
I would also mention that the movement of ceramics like this will also help Tank 3, in the case that you need to add more than just one or two fish to that tank in the future. Just grab a handful of ceramics from whichever tank has the most fish in it at the time and replace. Tank 3 will be good to go almost instantly.
Are you keeping up with your water changes on Tank 3 so that Jackson has clean water to heal in?