1)There is no such need to print sticker of UPC code on products. UPC is required for product listing and when you convert your stock to FBA that time Amazon provide you with a label that needs to put on product carton.
You need one UPC for one product and it really doesn’t matter how many products you are selling with it. For one listing you require one UPC code whatever its colour, size.
2)Yes, you can go with Trademark registration. In private label it is mandatory. But you can apply for it in second phase also. You can list your product by using UPC. You can have any name as you want.