Can't tighten thru-axle Long story short, my cone nut came off while riding.
Can I put it back without dismantling my freehub?
And why I can't tighten my axle anymore?

Only way I can tighten axle is without wheel. As soon I put on wheel (with or without nut), my axle will just spin around. I have removed rear wheel multiple times and never had this issue before.

Could I have lost something during a ride when my wheel came off? Or maybe I don't know how to put nut back on?
I suspect that with the wheel in the thru-axle is not aligned with the thread in the drive side dropout and isn't engaging.

If a nut came off your hub you really need to inspect the hub and check to see what else fell off. That looks like a locknut to me (can't see a bearing surface), if so you'd need to re-adjust the bearings at least.