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If you have to write one of these, which I do, are they simply a factual essay? Or are these used as another tool to evaluate your writing skills?

Also, should I include stuff like "I've learned ___ and ___ from this"? Or simply just state what happened?

Stick to the facts, for the most part. Don't do ANYTHING that could come across as whiny. However, if the incident resulted from something that was within your control, be sure to indicate it is behavior that will not be repeated. If it's illness, death in the family, etc. the facts should suffice.

P.S. If adcomms are reading something you wrote they are going to be evaluating your style of writing. In other words, if you have the choice between writing well and not trying to write well, why not write well?