All of your questions are ones for a for your Tax Accountant. NOT for others in the business.
And there might be some Accountant's here that can give some suggestions, but not know your business, there probably also going to tell you it is better to ask your Accountant.
Having said that, and NOT being a Tax Accountant.... I'm pretty sure the issue is because you've said you are PAYING yourself as an EMPLOYEE, so you are going to have to pay NYS SUI.
Also... According to NYS, you have to enroll in Family Leave if you have ONE (1) employee or more. So since you are paying yourself a salary and stating you are an EMPLOYEE, there's that word again, it sounds to me (not a Tax Acct) that you may have to pay.
As the Principal of the LLC you should be able to take a Distribution out of the company which is different that PAYING AN EMPLOYEE. But there are other things to consider as an employee, so again, Tax Acct.
And if you don't have an Accountant, this is why everyone suggests you do have one. Turbo Tax and the various companies that do your taxes real quick just don't know your business and deal with the big picture on recommending which path you should take on these kind of issues.
And where in NY.. Upstate, NYC/LI?