how can I inherit format when I create a new row or column in Apple Numbers?

The cells in newly created row generally take on the formats of the cells in the row immediately above, automatically.

Are you experiencing something different? If so a screenshot would help (shift-command-4, select area, release, and in a new post here insert the image using the icon that looks like mountains).

SG

I can't reproduce that here.

I selected Column C and set the Data Format:

Then when I add a new row that date format carries down:

SG

I am guessing that the difference between what you are seeing and what SGIII is showing is the way the cell format is set. If you type a date into a blank cell then go look at the cell format, it will be "automatic" with settings for date and time that match what you typed. That format will not carry down into a new row, the new row will be "automatic" with no date & time settings. You need to change the format to Date&Time for it to carry down (or change either the date or time setting and Numbers will change the format to Date&Time for you).