I share the same problems that you do and learned a few things that helps. Because your brain cannot feel the floor or sidewalk you walk on, it should cause falling problems. What I found is that if you look down, it helps your brain to understand there is something to walk on. In my case, my brain stops me from walking at all, till I look down and allow the brain to see it. Taking small steps helps the brain to remember there is something down there to walk on.

As for balance, side to side balance is not affected much but the front to back balance is dangerous and causes you to fall. Think of the middle of your foot as the place where your body balances itself. The front half of your foot keeps you from falling forward. The back half or heel is very difficult to balance on so you are most likely to fall over backwards. But if you are not careful, you may feel yourself falling backwards and lean towards the front and fall. I have fallen many times so I use two canes or walking sticks to help balance myself. Because the ground outside is uneven, be careful what you walk on because it will make you lose your balance. Hope this advice helps.