1. As for a machine i would suggest a flatbed with a walking foot like a old Juki 562 or 563. They are fairly common to find used in places like Facebook marketplace and craigslist.
2. I would suggest using a nylon bonded thread like Vimeyo. Personally I use number five for both hand stitch and machine stitching.
3. And by tightened, I'm assuming you're meaning a slight pucker when the thread is pull tight… That could be done by adjusting the thread tension of the machine…
One question you should think of is how would you care for the garment? As washing leather is never really a good solution… I guess there's always dry cleaning but I'm not sure how that works with textiles and a hide.
All that said, good luck