I need help formatting text for an InDesign project...

So you just need the names and dates to flow in a paragraph structure instead of a list structure? Can you just separate each item in the text box with bullets between them and no line break?

Well the thing is, I have quite a bit of text, and I’m not sure how to apply bullets and no line break for the entire thing. I only have a very basic understanding of InDesign so far.

You can do a Find/Change, from the Edit menu. You can look for an “end of paragraph” by choosing it from the popup menu next to the find field. Change it to space-bullet-space.

(This answer is assuming the text is all in one text box.)
Insert cursor at the beginning of the second line.
Backspace, which should put the second line together with the first.(technically, in the same paragraph)
Type (space *space) or whatever you want between them. Or go to type menu>insert special character for something fancy.
Do the same with each line.