when bot lane leave and stays mid

Bot should be mid to take the first turret, and then return to their lane when it's pushed in again.

The sooner you take those first turrets, the sooner the map opens up for your team.

It depends.

Bot should roam to try to get kills on mid or take turrets. They should roam back to catch farm.

Bot sometimes should switch lanes with Mid if Mid is a champion with TP or a assassin, or has greater waveclear then the mid laner. This allows the Mid laner to still gain solo xp. farm and be around Dragon and lets the ADC have a safer lane. This also allows the Support to be a better roaming threat top to bottom and allows the Jungle and Support to make coordinated ganks or invades for deep wards. (thus also allowing the ADC to gain some Solo xp)