Not quite. If a backend segfaults, postgres will detect it and immediately terminate all connections and exit. When it restarts, it will enter recovery mode.

Not quite. If a backend segfaults, postgres will detect it and immediately terminate all connections and exit. When it restarts, it will enter recovery mode. It does this because a segfaulted backend may have corrupted shared memory. The only way to fix that to restart in recovery mode and replay the WAL.