First don't try to blame them, accept your responsibility and admit your mistake, this way you will have much better chance to get an extension for your medicals.
Yup, but it's very good and really close to the TEF test. I've seen even the same texts and questions on Prepmyfuture as the ones I saw in the TEF tests.
IRCC is not supposed to mention all the reasons. It's enough to mention the first reason they encounter for a refusal.
Besides, the reasons may depend on a decision maker.
An invitation letter is useless for a visitor visa, it may even have the opposite effect.