Add periods when enter key is pressed

You could also create an EventScript with ExtendScript. That one could also check if you already have a "." at the end of the paragraph and only add a "real" period (not just a generated numbering), if that is not the case.

(I'm just wondering what the use case for this request it?)

What you could do:

Create a new paragraph format, e.g. "period" with autonumbering ".", at the start of the paragraph.

In the Pagination tab of the original paragraph with the text set Run-In Head. In the Basic tab set "period" as Next Paragraph Tag.

When you now press ENTER twice, you get your period.

For a single-sentence paragraph, you can use autonumbering to add any character at the end of the paragraph … but the character is then positioned at the right-hand margin, which probably isn't what you want :-}