Does keeping Torah and Mitzvot (commandments) in order to receive reward purify the heart? Or does it also purify the heart if one works in order to receive reward?

Mitzvot do not require intention, and even actions without intention can purify one's heart, but in the first degree of the desire to receive - which is the still of Nefesh de Kedusha (holiness).

Is the path of observing Torah and Mitzvot in order to not be rewarded meant only for a chosen few, or can anyone walk this path of observing everything in order to not be rewarded, by which they will be rewarded with Dvekut (adhesion) with the Creator?

Answer: Observing Torah and Mitzvot will turn our will to receive to be in order to bestow. This is given to everyone, without exception, for everyone was given this remedy. In the end, everyone will achieve their complete perfection, this is a matter of choice, some advance faster and others slower.

If a person sees and feels that he is treading a path that leads to Lishma, should he try to influence others so that they would tread the right path too, or not?

Answer: If he knows that he can reform him, then he must reform him, due to the Mitzva, and not for the purpose of dominating.