Precise meaning of "Last N days, weeks, months or years"

Tricky. On its own, last week means the entire previous week. So on a Tuesday, last week would be the previous Monday to Friday, or Monday to Sunday, depending.

In the last two weeks would generally mean the previous 14 days.

Today is Monday. Last week is strictly the period of seven days ending at midnight on Sunday and the last two weeks is strictly the period of fourteen days ending at midnight on Sunday. No one would refer to anything occurring today, yesterday or the day before as taking place last week or in the last two weeks. I wouldn't worry about it. As usual, the context will determine the words used and what they mean.

The singular versions (yesterday, last week, last year) are absolute.

"In the last year" is equivalent to "in the last 365 days before today", and thus includes the current year.

"Last year" means the last calendar year.

If I'm speaking on a Friday, "last week" includes 11 or even 12 days earlier, while "in the last week" is equivalent to "in the last seven days".

Such a phrase can either include or exclude the current moment, depending on how it's used. The phrase by itself represents a set of time points that can either be open or closed; closure, if any, is provided by the construction it occurs in.

Fillmore's 1971 Deixis Lectures cover this question among many others, in the third lecture, "Time".

The first two lectures in the series are recommended for background in reading this; these were actually delivered as a series of lectures, and such texts tend to build up ideas one by one, at the speed of vocal understanding, instead of compressing them into theories.

So it's serious linguistics, but it's actually composed in well-written English prose. With amusing asides. And real jokes. That got laughs, at least in Chuck Fillmore's deadpan delivery.