Does Mars contain more iron than the Earth? Is the reason Mars is red because its surface contains a lot of iron? (When dirt is red on Earth, it is sometimes caused by a high amount of iron).

If so, does Mars contain more iron than the earth?
Mars definitely has far less Iron than Earth. Mars has 10.7% of Earth's mass. On the other hand, Iron comprises 32% of Earth since there is so much Iron in its inner core, outer core, and the mantle. That means if Mars was made entirely of Iron (which it is not), Earth would still have more than 3 times as much Iron.

You are right that Mars has more Iron at its surface than Earth so it looks very red. Earth has many other metals on its surface (not to mention water to make it look blue and plants to make it look green).