If you can prove that you had the right to claim the child for that year, then yes. As far as the IRS is concerned, if you had physical custody of the child for 51% of the year (183 days) you had the right to the exemption.
As far as I know, homesteading in this way is a thing of the past. You can buy a home and then file it as a homestead, which helps keep it separate from certain liens and tax.
Homestead homes are located throughout Florida; from Homestead to the North of the city and as far as up the East Coast as far as Miami & Miami Heights. To arrange a viewing you can contact a local agent.
You can file as back as you want. If you owe taxes, the IRS will only prosecute up to seven years back, so it's recommended to only file the last seven years. If you are due a refund, the IRS will only refund the previous three years.
It is 1,444 miles according to Google Maps.
It is around 700 miles.
260 miles taking Florida's TURNPIKE (toll) - SOUTH.
The statute of limitations does not begin running until you file a tax return. So, if you haven't filed there is no theoretical limit to how far back they can go. Practical considerations may preclude going back an extreme length of time.
As far as I'm concerned, there's no way to get them back, aside from restarting your file. NEVER USE IT ON ANYTHING IMPORTANT.
287 miles
It is 33.3 miles according to Google Maps.
The one in Pennsylvania is 373 miles from Brooklyn. The one in Florida is farther.