LHR isn't in Schengen.

MCT is same for passengers and baggage and you don't need to think their job through for them. For a start, they will be already unloading bags before you deplane and will still be loading them on the next flight while passengers are boarding. I've had better luck over the years with tight connections than long ones to be honest, at least your bags are marked "priority" or "Shocon".

Having said that, 45 minutes doesn't sound right to me for an EU to south America connection. I'd expect longer times as detailed by nux.