When Mom dies do I have to be appointed executrix to get her tax refund?

IRS Publication 559 explains that: If no personal representative has been appointed and if there is no surviving spouse, the person in charge of the decedent's property must file and sign the [decedent's final income tax] return as “personal representative.”
https://www.irs.gov/pub/irs-pdf/p559.pdf

There is a line on the Form 1040 that allows for direct deposit of income tax refunds.

Turbo Tax has a discussion on "Death in the Family."

IRS Form 1310 asks whether you will distribute the income tax refund according to the laws of your state:
https://www.irs.gov/pub/irs-pdf/f1310.pdf

Assuming you're named as Personal Representative (or Executrix as f/k/a), you'll have to file a Form 1310 with the IRS to get the refund for her.

https://www.irs.gov/uac/Form-1310,-Statement-of-Person-Claiming-Refund-Due-a-Deceased-Taxpayer

I haven't filed this for several years, and w/o downloading the specific form I don't recall what other data you might have to provide. I believe that I also filed another form advising of representation of a deceased person, but it may have been in connection with a trust.

I would download the Form 1310 as well as any instructions, and determine what other information you might need to file it and get the refund.

I don't know what requirements the state of NY might have to get any state refund.

If your mom has a legal, valid will there must currently be a named executor - who is named?

POA ends at death. Executor takes over, as named in the Will. The IRS will not only want proof you are Executrix, they will want the EIN number of the estate.

I just checked will and I am named as executrix. How would i get a EIN #?

Call the IRS, or fax in the form. The EIN number would be for the Estate.

https://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/How-to-Apply-for-an-EIN

You could also benefit from reading this on filing an estate tax return:

https://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Deceased-Taxpayers-Filing-the-Estate-Income-Tax-Return-Form-1041

and this:

https://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Deceased-Taxpayers-Probate-Filing-Estate-and-Individual-Returns-Paying-Taxes-Due

Don't be put off by the small business and self employment aspect. The third paragraph in the link above explains the issues.

There's also a 706 form which has to be filed but only if the estate reaches a value of $1.5M, which from your initial post wouldn't affect you (and probably everyone who posts here).

My understanding of TurboTax programs, at least for individuals, is that they prompt with a lot of questions, so if you have an estate tax program with your TurboTax, it should help guide you through. (I've never used it; I do my returns manually as I prefer not to rely on canned tax programs unless they're professional ones such as those used by paid tax preparers or attorneys).