None of those is a main sequence star.
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.
Yes, the sun is a main sequence star. Main sequence stars are those, like the sun, that are fusing hydrogen into helium in their cores. This is the main stage of a star's life cycle when it is in a stable state.
A neutron star is a stellar remnant
main sequence
This happens when a main sequence star uses up all of its fuel and swells. Next stage: Red Giant.
the main sequence has a limit at the lower end because as a star's mass decreases, its core temperature and pressure decrease too. This eventually causes the nuclear fusion reactions in the core to stop, leading the star to move off the main sequence.
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
Sirius is not a single star but a binary star system consisting of a white main sequence star and a white dwarf.
None of those is a main sequence star.
The defining characteristic of a main sequence star burns hydrogen to helium in its core.
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.