What is the purpose of life on earth?

That's part of the general purpose which is to serve and glorify God and we do this by following Christ's or Buddha's teachings and being good to our fellowmen. To love God and your neighbor which in the end will glorify whatever Supreme being your religious beliefs dictate.

If all humans did that what a blessed Earth this would be but sadly this is not the case there is far too much war, greed and hate and selfishness on this earth and this does affect others but in a negative way. I don't think it's possible for humans to live side by side in peace. Peace is not part of the human pysche we always have to be attacking, feeling hate, anger and jealousy towards others. Maybe when this Earth is destroyed and a new mankind is created hopefully then peace will prevail and as you said love and sympathy will reign throughout.