Is it true that the sun will eventually become a black hole?

Not on its own. Left to its own devices, the Sun will eventually expand into a red giant, explode, and leave behind a white dwarf that over trillions of years would cool into a black dwarf and then very slowly evaporate under the process of proton decay. However, it is entirely possible that it some point it may be swallowed up by another black hole from somewhere else in the galaxy, whereupon its mass would become part of that black hole. Eventually, all the black holes will also evaporate due to Hawking radiation.

No. It's too small to become a black hole. It's even to small to become a neutron star. It is not big enough to go supernova. Instead it will become a white dwarf with a surrounding planetary nebula.

No, it is not true. The sun isn't massive enough or large enough to become a black hole. The Chandrasekhar limit is 1.4 solar masses

The likeliest ending is a main sequence dwarf star.

according to the best theory NO it is too small to compress enough

absolutely not.

if the Sun was 5x heavier, maybe.

No, it is not massive enough.

No.