Should I delete my accounts or essays on essay forums before submitting my applications to prevent colleges from detecting a ‘false’ plagiarism that may ruin my application?
You should not post them in the first place.
The plagiarism checkers aren’t limited to essays currently posted; an essay that was posted and then deleted will also show up. Hence all the warnings we constantly post here against posting your essay online.
To say nothing of someone copying your essay…
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Closing an account here only means that you can no longer access the account - past posts remain. As noted above, this is, in part, why we strongly suggest not posting essays.
Correct. There are many ways to find cached web pages, including cached pages of this site. One should always assume that once something is posted on the internet, it is there forever.