Strongman events are a lot of fun. I've had limited experience with those. Only done tire flips and farmers walks and stone carrying stuff...
Do the mobility drills before you start working out. They should take you 10 minutes or so. I assume you rest 2-3 minutes between sets while working out so between the mobility drills and actually starting your lifts you should get some decent rest. Usually I just do mobility work then set-up the bar for my lift, do a warm-up set immediately and then take a break.
It doesn't really matter either way. You just need to get your mobility work done before and I don't think you should wait too long (like an hour or so) after your mobility drills before you begin your actual workout.
To me a military press has always been a strict press. Feet being together, etc isn't really a concern of mine. It's like people calling a squat in which you grip the bar wide being different than a squat in which you grip the bar close to your shoulders. Completely irrelevant to the actual movement in terms of labeling it. To me, a press done in a strict fashion with a bar and executed while standing, is a military press. But then again, I use the term OHP and MP interchangeably because to me they've always been the same.
Conner is a beast!