You should stuff first and then sew on the buttons from the inside or outside. If you're still having trouble, you could use pins to mark around it.
I get safety eyes from www.crscraft.com
- better prices than what you can find on Etsy.
Amigurumi can be made however you want.
I've also used an I hook before. I like to double yarn or use bulky yarn though to save some time.