Q:

Do ships in Star Trek that can land on planets use impulse drive to reach space?

I have read many sources and understand that impulse drive can be very fast. A quarter of impulse can be way faster than the escape velocity on Earth (11 km/s) or on the Sun (600 km/s).
Does this mean that the impulse drive is used by ships that can land on planets, like Voyager, to get the ship back into space?
If so, is it therefore true that thrusters, struts, and dampers are what make starships have planetary landing capability? (All relate to helping the ship land, not propelling the ship to space.)

A:

Your question kind goes all over the place, but you seem to be asking, essentially:

Why does a ship like Voyager need special equipment to take off from a planets surface when the impulse drive is more than sufficient.

The answer is that the impulse drive is way overkill for lifting a vessel out of a planet's gravitational field into space. The impulse drive operates at something like 0.5 warp (150kish km/sec); you can escape from an Earth-sized planet for less than 5% of that. (The space shuttle, for example, only travels about 4km/sec while on solid booster). So, clearly the impulse engines are capable of pushing a ship out of even the biggest planet's gravity.
However, the impulse engines are not designed to operate in an environment with an atmosphere. The drive runs on an impulse reactor, a kind of nuclear reactor that, in order to produce its thrust, churns out the same kind of plasma, as the warp engines do. The plasma is so high energy, in fact, that the warp reactor output is one of the power sources used to run the ship; any excess is simply dumped into space via the "plasma exhaust".
In space, the plasma will simply radiate away as it cools, probably getting pulled along behind the ship. In a gaseous atmosphere, it could easily ignite the surrounding gas or cause extreme damage to any nearby structures or vegetation.
Instead, the ships use the much smaller kinds of gravitational nullifiers that smaller vehicles did in that time (e.g. anti-grav cars) to move the ship into a safe range to start up the real engines.
The other two things you mentioned have nothing to do with creating thrust:

The inertial dampeners were used to prevent sudden changes in the ships velocity from causing everything inside the ship to fly around. They basically counter-act the normal inertial behavior in the face of acceleration or deceleration of the ships hull. Inertial dampeners were always operating while the ship was in motion, they just need to be properly adjusted for the deceleration of a landing.
The landing struts are just landing gear for ships. You don't want to set the ship's actual hull down on a solid object, as it could cause damage and would probably not balance very well, so they put out struts for the ship to rest on while immobile.

