Yes they do make them and they seem pretty old school. I would stick with what you have. I have a board with the click-in system and they are really hard to get locked back in when you have snow packed into your boot or step in area. I wish all of the time I had the other system!
I'm sure they do because it's burton. If you want to replace your bindings, i recommend getting strap in's since I've had bad experiences with click ins i.e. not being able to click in to them lol (ice forms = bad night).
Yes they do. I've tried the click in and the buckle and found that the click in is more prone to freezing. Snow and ice can get into it and I would end up wasting time scooping it out before I could get my into it. Ideally, it's up to your preference but I would take time and look at reviews before choosing one.