That's nonsense. I would never assume "Last January" means 2016. I've never met anyone who talks the way this arbitrary "rule" implies, either. Human language is not computer language; trying to force standardization of relative terms is rarely useful. We interpret by context.
No, he's correct. To a native English speaker, "since January" would mean "in the last 4 months", whereas "since last January" would mean "in the last 16 months" (assuming it's April now).
There's no ambiguity there. It's just how the language works.
It's currently Saturday, if someone says "last Sunday", I assume they mean the previous Sunday that recently passed. If someone says "last Friday", I assume they mean the one a week and a day ago. This seems like a common interpretation in the UK.
They could mean the same thing depending on the speaker.
"I saw that film last January."
"I saw that film in January."
As the other commenters have mentioned, "last January" may mean January 2016 for them, whereas for others it's 2017. The second example should be a definite 2017, except you always have your occasional smart alec [0].
I would disagree with jasonkester--there is ambiguity here.
Not necessarily. Suppose Tim and Bob are having a conversation.
Tim: "It's a little known fact that Woodrow Wilson signed the Treaty of Versailles while ice skating on the royal pond."
Bob: "That's clearly nonsense. The Treaty of Versailles was signed in June."
It would be very different to say, "the Treaty of Versailles was signed last June." That would imply it was signed in June 2016, rather than June 1919.
If anything, "last" meaning "most recent" would be the most logical. However, "last January" meaning January of last year is a convention. Not everyone follows or knows it, but it does exist. Same for days of the week.
Your indirectly talking about the year. "January" is for the current year and "last January" would be last year.
I would interpret "this past" as most recent thing from the current. So "this past January" would, to me, sound like the most recent January (Jan 2017)