1. You can apply for a kindergarten on website. Denpending the commune you live in, at least in CPH, the only required informatin is CPR number. I think you can try to start applying. There's potential problem, the commune department responsible for processing your case may see the family registration information and if your child is not registered as a resident currently living with you, they may not approve your application.
2. Depending on where you live, you can easily see on the website how many children are on the waitlist. It could be as long as several month or as short as a few weeks.
3. Please don't ask back which is the website for application. Do your diligence and it's easy to find them with google.