The defining characteristic of a main sequence star burns hydrogen to helium in its core.
No. Red giants are not on the main sequence.
A red main sequence star would be a red dwarf or a branch red giant. To be on the main sequence, you have to have hydrogen nuclear fusion.
The sun is a main sequence star, so 1 AU.
Main-Sequence star
None of those is a main sequence star.
Sirius is not a single star but a binary star system consisting of a white main sequence star and a white dwarf.
Most stars are on the main sequence; that includes red dwarves. Specifically, in this case, the closest known star - Proxima Centauri - is also the closest main-sequence star.
Algol is a blue main-sequence star in the constellation Perseus
When a star "goes off the main-sequence" it generally means the star has run out of hydrogen fuel and is beginning the post-main-sequence or its end of life phase. The main sequence of a star is the time where it is no longer just a proto-star but is burning hydrogen as a primary source of fuel.
Any star that it fusing hydrogen into helium is classed as a main sequence star.
main sequence star
Unfortunately, it is impossible to tell accurately where a star is on the main sequence.