Learn English – since this Monday/since Monday

I agree with Tetsujin; native English speakers differ. I've heard native speakers use both meanings in each of the examples you give. I most often hear "this Monday" and "next Monday" to both mean "the Monday of the following week". And of course contextual cues can be used to determine if the speaker is intending "this Monday" to be in the past. "This Monday the weather was so nice I washed my car" is pretty clearly in the past.

I personally am in the habit of saying "this past Monday" and "this coming Monday" to clearly indicate which I mean.

This is a good lesson that you can't always trust what native speakers write. Of course, sometimes it's impossible to know if the odd grammar is just slang or laziness.

You are correct, and the sentence should be:

I haven't been able to sleep well since last week.

to indicate an ongoing condition, or simply

I can't sleep well.

to indicate a present condition.