Would added mass to a star make it turn into a black hole?

No

It would just make it a Bigger Star

Although, the bigger the Star the bigger they Blow

To add enough mass, you'd have to add other stars, you couldn't gather enough rocky matter locally. Our sun, for example, contains 99.86% of the mass of our solar system. If you took everything else in the solar system and dropped it onto the sun, it would have very little effect.

No, not necessarily, and not immediately. Sometimes in binary stars enough mass is added that the more massive star becomes a neutron star when it goes nova, but not a black hole. It does not go Supernova.

Solitary low mass stars like the Sun become white dwarf stars with planetary nebulae after the helium flash after the red giant stage.

Low mass stars, like the sun, do not supernova. They just burn out and shrink to be a white dwarf. Stars more than 3 times the sun's mass supernova and the core shrinks to become a white dwarf or neutron star. Huge stars supernova and their core has so much mass that it collapses to a point and becomes a black hole.

Throwing some planets into the sun.wouldn't do anything You need a star many times the sun's mass to make a black hole.