We have used them on our solid oak floors (not pr-efinished) and have had no problems, it's actually quite cute and hilarious to watch them in our cold Chicago winter :) These have never been used outside, so we weren't concerned. After we can use them outside, I will have to see if the wheels are scratched up and then they will not be used inside any longer. However, if you do not have solid, or have a softer wood like walnut, I probably would not let them be used indoors.
mine are wide as well, I'm guessing so they can accommodate all types of shoes. But when I tighten the skates, I actually bend the plastic edges somewhat so they create a narrower area. My daughter is in a size 7 toddler shoe and i can usually narrow the gap significantly to stop the majority of the sliding. I pinch the edges while I strap the velcro. It works for us.
Sure, if you child can stand/walk with some stability they should be fine. The wheels really roll though and if you don't have them locked your child is going to fall - I suggest helmet, knee pads etc. These skates grow with your child as the size is adjustable. I love this product.
There are three settings that you can switch between, which allow your child to go from walking to actual skating. The skates are pretty good. They are sturdy and easy to put on and take off. My daughter loves them.
They are meant to be used with shoes. In other words, put his/her feet in tennis shoes, or another closed toed shoe, THEN strap the skate in place. My 3 year old has very narrow feet and these are still just fine with her tennis shoes on. Hope that helps.
My granddaughter is over 3 and wears a size 10. They are set on the smallest size so I'm sure they fit way beyond a size 13. They can fit me. We love these skates. They can be set so only the front wheels turn. Then both wheels turning but not totally free wheeling. The third stage is totally free wheeling as the child cans confidence through the first 2 stages.