Lots of issues but think they all have been covered. It looks like the old and new panels are the same brand (labels are hard to see in the second pic). Should have kept the cable clamps and could have reused some of the old breakers instead of all those duals. Why all the duals in the new large box?
The cable below with the sheath short of the box - if the wire can't be moved so the sheath can be clamped to the box you are going to have to enclose the individual strands. Might be able to use a short piece of conduit with a clamp on the lower end.
Not clear how the lower metal flex line is attached to the box - it's hidden by the drywall. Guessing it may not be properly clamped based on the other things that can be seen.
Yes, old and new panels are from Square D. Not sure how old is the old one though but it almost appears that it came with the house - house was built in 1968 FWIW.
For breakers, I was just matching to what was already there - if it was tandem before, I just went ahead new Tandems. The old breakers and new panel weren't compatible - the old ones were slim and when I tried putting them on new panel, they were not secure and just dangling on the spot which didn't feel safe to reuse.
The cables below, one in the center - its for the electric stove and that isn't used anymore as old owners moved to gas stove. I plan to keep the wires so in case in future we move to Induction, which I feel won't be done until its forced upon us.
The next set of cable with yellow electrical tape - its 8/3 NM cable that is wired to AC. This wire goes in behind the wall to crawlspace and outside. Since its not code to use NM cable for crawlspace, I am going to take it out and move it 8AWG THWN (separate R/B/G) and run that in conduit.
The lower flex metal is empty - I will cut it off. I don't know what tool to use to cut it off ( and I am researching the name of the tool).
So for the bottom - there will be existing stove wire (which the conduit needs fixing) and then new set of wires and conduit for the AC. I just got the wires delivered to me today, so will upgrade the AC wires this weekend, weather permitting.