Phrase Usage – Can ‘The Other Day’ Refer to Several Months Ago?

The question needs context. You need to ask your friend for more clarification. Relative dates can be quite confusing. If your friend wanted to be more precise in his question, he could add "from today".

"Last two weeks from today" means the last 14 days. Whereas "The last two weeks" could have many meanings depending on context.

Consider this scenario. Today is Friday, February the 3rd. I ask my friend "What are you doing this Sunday?" which would imply the next Sunday on the calendar (Feb 5). Or I could ask "What are you doing next Sunday", which could imply next week (Feb 12). Even though I asked about "next Sunday" it's not actually the next Sunday.

If somebody asked you "Where did you work last year?" they likely wouldn't mean literally all of 2016 or even the previous 365 days. There would likely be more context to it. Consider this conversation.

Judy says

"Thanks for coming to visit me on my Birthday!", to which I reply

"My pleasure! It was easy for me to get here because my new office is just around the corner."

"Where did you work last year?"

"On the other side of town."

Judy isn't asking me what my job has been for the last 365 days, she's asking me where I worked on her birthday last year.

It is a confusing topic that native English speakers still get confused about.

In your specific scenario, it wouldn't be rude to ask him "Do you mean this week and last?" or "Do you meant the last 14 days?" or "Do you mean last week and the week before?". I personally have found it common to ask for clarification of dates in casual conversation. Legal documents and conversation where it really matters would likely have explicit dates.

Computer systems like Stack Exchange or Facebook are stupid and are (generally) programmed to always round down to full hour increments regardless of the proximity to the subsequent hour.

As such, it's necessary to ascertain the actual time the post was made if you really want to know how long ago it is.

In actual usage, no human would say that something one hour and fifty minutes ago happened "one hour ago". We are smart and know that one hour and fifty minutes is nearly two hours so we either round up to "two hours" or we say "almost two hours ago".

Generally, at the very least, we go in half-hour increments. So, something that happened an hour and thirty minutes ago is "an hour and a half ago". We distinguish events that didn't quite meet that time frame by using "less/more than" or "about" or other words that note that the time is imprecise.

In practice, people may be as precise as rounding to every ten minutes... so if something happened one hour and 42 minutes ago, they might say "about an hour and forty minutes ago" they might also go to the quarter hour "about an hour and three quarters ago" or to the full hour, "almost two hours ago". All of them are valid. I attest that it would be considered rather unusual to say "one hour ago" in this case.