For instance, if you weigh 180, is it realistic to shoulder press 90s overhead or should one stick to pressing bodyweight with the barbell?
Is it realistic? Yes. In fact there is a Strongman event called the circus dumbbell.
There is a proper technique to getting that bell overhead, and the folks at Lift Big Eat Big have a good article on how to do it: http://liftbigeatbig.com/mastering-the-circus-dumbbell/
The technique high points include:
- Clean the dumbbell to your shoulder with both hands
- Rotate your elbow out, resting one end of the dumbbell on your shoulder
- Jerk the dumbbell up
You'll find the big trick is to get under the dumbbell as soon and as confidently as possible.
BTW, the circus dumbbells can weigh over 200 lbs. I have a loadable one, and completely empty it is 135 lbs.
I haven't seen the double-half-bodyweight dumbbell press before, but it seems like a perfectly reasonable feat of strength. Since plenty of people can press more than bodyweight overhead using a barbell, I think doing so with dumbbells is within reason. Just like pressing bodyweight in barbell form, it will take a good deal of work.
By realistic do you mean functional? Either case no. The overhead press is typically one of the weaker lifts as it uses smaller specialized muscles in a motion that is not typical of daily life. But I figure that is not what you mean.
By realistic do you mean plausible? Absolutely. While it would be easier to lift bodyweight (plate's and bar) rather than bodyweight plus the bar, you can train for either and I'm sure you can get there. That being said, it would be rather difficult but not un-doable.
Be safe lifting and have fun.