About the Statue called Laughing Buddha...
The Statue called Laughing Buddha is not Lord Buddha or any Buddha. He is some local divine figure in some culture in the east and this statue is misunderstood as a Buddha because it has a name that sounds a lot like Buddha. It's correct pronunciation should be like this or something close - Laughing Budhai
About the Greek connection...
The statues were not made by the Asian artists because of respect and the fear of their creation being not god enough, This should go withot saying Gauthama Buddha was considered the most charming person in India and people even became monks just to see Buddha's beauty.
As the story goes the appearance was unique and it was not alike with any other person (But as the suttas say only The great arahant kashyapa looked a bit like Lord Buddha). With the scientific knowledge we have today we can say the DNA structure of a Lord Buddha is either unique or a complete anomaly.
A king called Kanishka who ruled a certain part of India took a Greek wife and with her came a lot of people as it was a tradition to send skilled people as gifts with princesses who marry to countries abroad.
At the time Buddhists had many other depiction of Lord Buddha to worship Like the "Anandha Bodhi" - Video and Lotus carvings on rock pallets.
The princess questioned the king Kanishka why there is no statue of Lord Buddha in his kingdom and the king explained why. So she ordered her people to create a statue and with time finally Asian artists came up with their designs.
Why Buddha is not bald and what was the appearance of Gauthama sage?
When Prince Gauthama started his journey he used his sword to cut his hair. But later on even though Lord Buddha advised monks to shave the hair there is no mentioning about Lord Buddha shaving hair. This should go with the special look all the Lord Buddhas shared "The hair with very small curves." A lord Buddha never appears without hair and the unique hair is sign for others to know who it is.