OSD_FULL: one or more OSDs full
Ceph has blocked writes rather than fill an OSD completely. You do not free space by deleting at random: raise the threshold temporarily by a hair to get I/O moving, free real space, then put the threshold back. Whoever raises it and forgets ends up in the same place with less margin.
PG_AVAILABILITY: placement groups not being served
There is data no OSD is serving, usually because more OSDs are down than the pool tolerates. What matters here is working out whether those OSDs are recoverable before declaring them lost: an OSD that is merely powered off is one thing, an OSD marked lost is irreversible.
MON_DOWN or lost quorum
Without monitor quorum nobody decides anything, and I/O stops even with every OSD alive. The usual causes are two nodes lost out of three, clocks out of sync, or a network partition. Start from the monitors, not the OSDs: until there is quorum, acting on OSDs achieves nothing.
PG_DAMAGED: inconsistencies found by scrub
The scrub found copies that do not match. ceph pg repair often works, but first work out why they diverged: if the cause is a disk corrupting silently, the repair is temporary and the problem returns.