Apple numbers formula for date on the nth day of a given year

This is pretty easy. Numbers will happily add dates and days, so all you need is one cell (or calculation) that determines year, and another cell (or calculation) that has the day number.

For example:

Cell B2: year
Cell B3: days
Cell B4: =DATE(B2,1,1)+B3-1

The DATE() calculation works out the first day of the year given in cell B2. To this, you simply add the number of days from B3, and subtract 1 (since day 0 is the first of the year)

If you want the result to show the month name and no year you can just use cell formatting to display the date in whatever format you want.

If you specifically want '3rd March' (with the 'rd', 'th', 'nd', etc.) that's going to be more work...