How do colleges view things that can’t really be proven? Like some people write about trips, or getting hit by a car, or doing an internship, but I’m thinking of writing about things and activities at home that can’t really be proven that I actually did them. Will colleges not really take my essays seriously?
An often-repeated advice here is that it is not what you write about but how - with some exception for taboos, like badmouthing parents/teachers, self-pity, etc.
Other parts of application will give you opportunities to list things that can be proven.
Agree with @ArtsyKidDad- the point of the essay isn’t the specifics but what the overall message conveys about you as a potential member of the college community. In a really strong essay you should nearly be able to change the ostensible topic and the essay would still show the important parts of your message. A recent Princeton Admissions Director waxed lyrical about an essay about minding younger siblings - it wasn’t the fact of the activity, but the narrative arc through which the student showed a beginning, a moment of realization and then how s/he had acted on that realization since then.