Final answer:
After it experiences a helium flash, a star like the Sun does not increase significantly in luminosity, grow larger than it was as a red giant, return to the main-sequence position on the H-R diagram, or fuse the heaviest elements in its core.
Step-by-step explanation:
After a star like the Sun experiences a helium flash, it enters a brief period of stability where it fuses helium into carbon, and sometimes oxygen, in its core. During this phase, the star's situation is analogous to the end of the main-sequence stage, but with more complexity in its internal structure. The release of energy from the triple-alpha process causes the star to decrease in luminosity and to have an increase in surface temperature. Consequently, on the H-R diagram, the star moves to a position that is to the left of and somewhat below where it was as a red giant, but it does not increase in diameter or luminosity, nor does it return to the main-sequence position. Moreover, it can't fuse the heaviest elements like iron or gold; those processes occur in much more massive stars.