Yes you can operate a daycare in an apartment. Some families may be turned off as you do not have green space easily accessible
The big advantage to private is you get to keep all your money. Downside would be you need to find all your clients. I am private though and have never had a real problem finding people.
Peer networks- here and Ottawa (can't remember the name at the moment)
Re: your specific focus- this will really limit you and as a sole provider makes it difficult to offer good care to multiple children with special needs. Also, the number of kids diagnosed with LD's etc prior to starting school is also far far fewer.