should I take myself down to a level where I can do all my pull-ups with good form and work from there?
That's what I would do but it's really up to you. You should be taking time off and de-loading anyway, that is dropping to a lower level and doing that for a week. I got injured at Level 7, took two weeks off and dropped to Level 4 and then increased the level every until I got to Level 7 and my times were much better.
On day three, are the pull-ups/pushups/squats each meant to be performed in solid blocks, or can I break them up into subsets (as I have been doing)?
You should be staying 1-2 reps below failure when doing them. Like on Level 7, there's no way I can do 40 straight pull-ups. So I do maybe 15 straight off, rest a few seconds, hit 10 more, then maybe sets of 5 until I get 40. You basically do as many as you can until your 1-2 reps away from missing, rest, then do more reps in that manner. So yeah, you can break them up into sets but don't be so rigid about the numbers, try and push yourself to increase the number you can do before failure. So if one week you try 26 pull-ups and do 5-5-5-5-3-3, next week try 7-6-5-5-3, then 8-7-6-3-2, or whatever, as long as you don't reach the failure point.