Main panel feeds this sub panel.
-No over-current protection on sub panel feeders
-Separate grounds and neutrals on sub panel bus bar
What else?
Those are both “sub” panels based on what I can see, and they’re both wired improperly.
The first picture shows an equipment grounding conductor to the neutral terminal (which is improper) and then a bonding conductor connecting the neutral terminal to the grounding terminal - again, improper.
In your second picture, the equipment grounding conductors are not bonded to the enclosure/panel. They are attached to the isolated neutral terminal, which is improper. In addition, the neutrals and grounds are sharing the same terminations, which is also improper.
Judging from the conductor size it appears that the top right 2-pole CB is the main which is backfed. Is there a service disconnect ahead of this panel? If this panel contains the service disconnect then the jumper between the EGC bus and the neutral bus is OK.
Main disconnect is the top right breaker, the top conductors lead to a service panel.
So is this the service? What do you mean by a service panel? Anything past the service disconnect is considered a “subpanel”.
I considered that, and if that’s the case, then the direct tap to the lugs (with no OCPD) is improper.
If the 2 pole CB is a back fed main then the conductors under the top lugs would only be protected by that main. You’re correct, that unless the installer has complied with a tap rule those condcutors are likely protected at an ampacity that exceeds their value.