How much iron would I have to shoot into the Sun to blow it up?

First, a minor correction: iron is not too heavy to allow the reaction to continue, it is incredibly stable and therefore cannot produce anything else (it would take $\sim10^{22}$ years for it to decay into chromium and its binding energy is the highest per nucleon, so it would "cost" more to produce something heavier than iron has in it). Research shows that once silicon is produced in the core (silicon produces iron), the star has about a week before it blows up!

However, in order to produce that in the core, the sun needs to be about 6-8 times our suns mass. So rest assured that our sun will not go supernova (though it will go through a red giant phase and swallow earth in about 5 billion years).

The boiling point of iron is about 3000 K (5000 F) while the surface temperature of the sun is about 5500 K (10,000 F), so this comet-of-iron would evaporate en route to the sun's surface.

No, it is not true. This is not how fusion in stars like the sun works.

The sun is fusing hydrogen to make helium. At this point any other reactions are very rare, not sustaining, and irrelevant. It is not true that a whole chain of higher elements are being created at this point.

It is also not true that iron is too heavy to allow nuclear reations. Iron happens to be the low-energy point, so there is no net energy gain by fusing it with other elements, or fissioning it into other elements. It is possible to get energy by fissioning much heavier elements than iron, like uranium and plutonium.

After the sun has used up its hydrogen and is mostly a ball of helium, it will first collapse a little. This heats the helium so that now it can fuse. This releases more power than the original hydrogen fusion did, so the sun expands to become a red giant, which as one of its side effects will engulf and incinerate the earth.

When the helium runs out, a whole sequence of other things happen. For stars of the mass of our sun, there won't be a supernova, although there will still be a sizeable bang before the nuclear reactions cease and it cools down and becomes a dwarf.