Two planets which collide will affect Earth because the mass of the new planet is larger than the two individual ones, but how much the planets affect Earth depends on how close they are. Any planet or thing that has mass has a gravitational force associated with it. If the collision causes the new planet to move towards or away from Earth then that can affects us because planets which are further away have a weaker pull on us than those that are close.

The universe is huge. It would probably not affect the earth. The probability is really small that a planet leaving its solar system would come close to the earth.

Planets do sometimes collide with each-other, although they cannot "break out" of gravity (gravity extends throughout the entire visible universe). Earth's moon probably formed when the Earth got hit by a planet about the size of Mars early in its history. This would have destroyed all life on Earth if there had been any at the time. However, had there been any life on the real Mars, or on Venus, at that time, they would probably not have even noticed.