Technically speaking, an early start is important.  Children at a young age have good memory powers, nimble fingers and quick coordination.  Training to channel these characteristics into piano playing is no different from training a child to ski or skate at age 3 or 4.  The earlier the training, the better to nurture a budding talent.  This is not to say that those who did not start early are doomed to failure.

Music training however, does not necessarily mean starting on an instrument immediately.  Pre-school kids or toddlers can receive training in music through rhythms, note reading, ear training in the form of play or games to motivate them. There are several schools that have music classes for pre-schoolers that are aimed to introduce children to music.  Through listening, the children can be trained to appreciate music.  This is very important, teach your kids to appreciate music first, before introducing them to an instrument.

 

2.  Should parents push children to practice?

What child would not prefer to play outside than stay indoors and practice the piano.  There are many instances when adults wished that their parents pushed them a little more in their younger days when it comes to piano practice.  I would prefer using the word "coax" than "push".  Parents can participate in the musical upbringing of a child through motivation, encouragement, coaxing, rewards, etc. 

3.  How can parents help with the musical upbringing of a child?

In Europe, there is a seriousness about music that's not common here.  There, children grow up with classical music, surrounded by magnificent historical buildings, museums, art and culture.  Parents can provide inspiration to children by playing music of all types to introduce children to music.  Children can develop music structure by listening, and learn to appreciate the beauty of music.