from - used to show the time when something starts ...
The library is open from Monday to Friday
The new rule will apply from September 1st.
over - during something, or while doing something
We were in Italy over the summer
I have been very busy over the last few months
since - from a particular time in the past ... until now
I have been working here since 2012
I haven't eaten since breakfast
from is used to specify when something started (you can use since as well for this, if it is still happening) or when something will start.
over is used specify a period of time- usually while something else is happening.
Your first sentence is therefore best written as:
All because of my fine efforts over the last 2 or 3 months.
For the other three sentences, they are all in the past, so if the situation still exists it would be better to use since.
since 2 PM
since last year.
We don't really say "since last minute": a minute is to short a time interval for from or since. You might instead say something like
I only started a minute ago.