Hi one assumes by the addition of the pictures you have the technical sheet for this watch. As mentioned by @HectorLooi center wheel canon pinion .take it down again and install only the parts required to set the hacking and turn the hands checking at each stage for correct operation.
Hi if it is a Swiss made watch badged by ingersoll (eubauches) ther is likely a makers mark and number under the balance that may help . If you open it up and post a picture of the movement plus Any numbers.
Width of the opening is about 19mm. I only use it for parts like the escape wheel.
Cap jewels are hard to find. So I usually put a drop of fixodrop in a small glass bottle (5ml), then hold the cap jewels in tweezers and dunk. Similar with pallet jewels - I hold the pallet with tweezers and dunk just the jewels.
I used do it by pushing the pallet in to some pithwood, jewels up, and sit the cap jewels on the pithwood, then using a small syringe, drop some Fixodrop on. But this method is more wasteful of the precious fluid. Using the small bottle I can tip it back.