He was most likely wiped at least once since then

Yet some memories remain probably

Possibly

Not possibly, they do. He remembers becoming an Exo, Dr Maya Sundaresh, etc.

They don't remember everything. He could've wiped that from his memory so it's still possible

They're not wipes, they're reboots. To use Cayde's own words. [quote]See, the reboots, they don't wipe it all away. Not everything.[/quote] Cayde also has unpleasant memories, such as [quote]There's no bounty. No Hive. I'm out in plain sight. Sky is torn open and there's nothing and nobody left in this ruined world but me and the boiling shadow all around. Whatever it is hits me before I can level my gun. Doesn't matter. Tendrils of pain crawl over my splayed fingers, my outstretched arms, my shoulders, my neck, my screaming mouth as it consumes. I'm being enveloped. Everything is wrong. Primordial. My systems go sideways. All but my sensors. It wants me to witness this, the world.[/quote] Which maybe from the collapse. Cayde tells us that Exo's try to forget, not that they wipe away unpleasant memories. Exo 2 also shows that they have buried memories, memories that include the collapse.