It is recommended to greet all Muslims whether they were practicing or not. It is better to offer help to believers whether they were practicing or not. Also it is better to socialize with people in good manner with people who practice Islam and with the ones that do not. It appears in some of the narrations that the good behavior deserves great reward.
It is not necessary to use the hands in washing the face and arms during wudhu. It is valid to wash them by placing them under the tap directly, such that they are washed from the top downwards. It is also a condition of the wudhu to wipe the head and the feet with the dampness on the hand that originates from the wudhu process only, and not to allow the hand to become wet from other than that before wiping.In light of the above, before one proceeds to wiping the head and feet, one should ensure that a part of the left arm is unwashed before using the right hand to wash the left arm, in order for the right hand to have only the water of wudhu on it. Otherwise, the water on the right hand might be extra water and wiping with it will invalidate the wudhu.