Hi,
Iam about to start phase 3 on the beginner template. But as for exersice selection “vertical press” is overhead press and “supplemental press” is dumbell press. So now overheadpress is 12reps sets and dumbell press 6reps sets. Since I prefer to go heavy on barbell movements more than on dumbell movements, can I swap them out, so I would do 12 reps dumbell press and 6 reps overheadpress?
Sure. You can also change the exercises to your liking 
On a related note (pressing movements): What would be your assistance selections in Beginner Phase 3 which you deem best to improve the competition bench?
I probably wouldn’t be focused on improving the “competition” bench in this context, but to answer your question: 2 and 3ct paused bench, close grip bench, touch and go bench, and pin bench.