First question: are you a citizen, or green card holder? If so, you will have an ongoing oblication to manage this, until you renounce your citizenship, or as long as you want to maintain your green card. If not, then you also could have the option to set up accounts as a non-US resident.
Residency does not have a single definition--it is a matter of opinion. But New York, being a high tax state with a lot of non-resident taxpayers is very...active...in this. The best way to insure you don't end up with a tax or legal headache is to look at residency rules (for tax purposes) in both NY and FL.
A quick Google confirms NY's strong gravitational pull on your tax dollars. You need to make sure you have met their requirements to *not* be resident. (or, specifically, not domiciled for tax purposes) Fortunately, they have documented how:
https://www.tax.ny.gov/pit/file/pit_definitions.htmWhile Florida is somewhat more easy-going, there is a process there, too:
https://www.stateofflorida.com/residency.aspxSo some of the things are obvious: change your driver's license, change your voter registration. But those facts aren't absolute. Certainly, changing the address for any business correspondence you have also adds weight. But simply registering to your Brother's address won't do it, either, although that may be a better choice than a mailing service. You need as much evidence of your identity as possible to point to where you want to be established.
In a quick scan of NY form IT-203, I do see a hopeful exclusion to NY taxation for non-residents:
interest, dividends, or other income from intangible personal
property, or gains from the sale or exchange of intangible
personal property, unless the intangible personal property is
employed in a business, trade, profession, or occupation in
New York State;
Maybe this means you don't need to worry about going to the extent of changing residency. But, when the time comes to make withdrawals from your 401k, understand that *will* be income, not capital gains, so if you are NY domiciled, they will want their slice of that. So I think the answer to question #3, if you don't take action, is yes--you would still pay NY taxes, even with an alternate mailing address. But this will cost you when you withdraw your 401k, the full amount of NY's tax rate.
In the end, I think it's best to work with a CPA, at least for the transition year and first full year. Even if you mean to manage this yourself in the future, they can give you a pattern to follow. And maybe you won't trust yourself to follow through on all the necessary documentation, or keep up with the changes that will occur over time. It will be expensive, but that's the cost of such an adventure.