Do mines re-spawn? My guess would be no. Logically, veins are static; they don't grow like plants do. But I've noticed that sometimes logic d/n really have a place in gaming, lol.

I've heard that veins replenish every month, but haven't confirmed it myself.

It's 30-40 days

Yeah. Every 2-3 weeks.

Along with, if there is, Bandits, ingredient's and loot.

But you have to be away from the area. Far away i mean.

Mines with enemies get the cleared flag and uses 30 days to respawn, mines without enemies respawn in 10 days, note if you don't get cleared it's 10 days even with enemies.

Real world mines does not respawn ore, however you can mine them for years.