Will Mercury eventually be pulled into the sun?

Mercury, like the other planets, is in a stable orbit around the Sun. A planet's orbit is a geodesic through curved spacetime. A geodesic being the 4 dimensional equivalent of a straight line.

The only way a planet's orbit can change is if another body's gravity causes it to move. If planets move they tend to move further away from the Sun. So, Mercury is unlikely to fall into the Sun.

In about 6 billion years time, the Sun will run out of Hydrogen fuel in its core. At this stage the Sun will expand into a red giant. As the Sun expands it will consume Mercury, Venus and possibly the Earth.

No, Mercury will not be pulled into the Sun. While Mercury's orbit is gradually shifting closer to the Sun due to tidal interactions and other factors, it will not be pulled into the Sun because its orbit will stabilize due to the balance between gravitational forces and its momentum.