Assalam'alikom
Is it right to help a Non-muslim? And do we get any reward in doing so?
Jazakallah..

Since this is asked in society not Islam, I will address it.

We do not do things for others to get a "reward" we do it because we wish to be kind and to help others.

The rewards that you receive for helping a fellow man are within yourself. Knowing that you are good without feeling pride, spreading the purity and kinship of your religion through actions rather than words. I am a universal blood donor (O+) because I feel it's my duty to help anybody who needs my blood... my blood does not discriminate against race, religion or physical/mental ability. When in the Navy my oath as a Hospital corpseman was to help others without limitations as to who should receive it.
Too many people waste time asking themselves if they should help when the answer is obvious.
I'm not Christian, I'm not Muslim, I'm not an Atheist... I'm just a guy, a plumber. Practicing the life that I hope my daughters will practice to make them and the people that they meet happy in life.

Wa `aleikumus-Salaam.
In some cases it is obligatory, other cases it is forbidden, and some cases it is a good voluntary act that you are rewarded for.
From the obligatory (If you do them seeking to please Allaah, you have reward. If you leave them, you have sin) are:
-parents and relatives
-neighbours
-travellers
-orphans
-poor people
-the oppressed;
From the forbidden are:
-helping the enemies of Islam against muslims
-helping a person commit a s

... a sin, such as any form of disbelief or shirk, adultery and fornification, stealing, involving in alcohol, drugs, usury etc;
And from the preferred good deeds are for example:
-helping an elderly person accros the street
-generally all good, polite manners
-giving benefitial advice
-medical assistance
-all acts of mercy and kindness that are not forbidden or leading to forbidden
-praying for them (but you shouldn`t forget especially to pray for their guidance too)
-forgiving those who do injustice you personally
-calling people to all good, calling them to Allaah, and establishing to them means to ease their affairs (which may actually be mentioned on the obligatory side)
-being friends and behaving well and righteously with those, who do not oppose Islam is allowed
-loving to all people (not only to muslims) that which is beloved to yourself is a sign of being a muslim
And Allaah knows best. Forgive me, and may He forgive us.