Yes, it’s possible. Fabrics do breathe. However this may or may not stop you getting damp under your jacket.
For this, you need something to wick the sweat away from your skin, then any other layers need to be able to wick too, then the jacket has to be able to shift as much moisture as your body’s producing. If any of those things don’t happen you’ll get damp. Most breathable fabrics are not breathable enough to shift the copious amounts of sweat a fat MTBer will produce.
If at any point you think your jacket’s not breathable, go and get an actual non breathable one and test the difference.
It’s an outer shell, who cares if it’s a bit dirty?
It does. Dirt affects performance, especially if it’s eVent, don’t want those tiny holes blocked. And you don’t want the dirt inside eroding the delicate membranes either.
Because it will get filthy the first time you use it*
If it’s wet enough that you plan to wear a jacket, put mudguards on.