Can I put (4) 60 watt bulbs into a ceiling fan instead of the (4) 40 watt bulbs that the fixture is asking for because it is not enough light with the 40 watt bulbs

Don't do it. If the fixture calls for 40 watt use 40 watt. You definitely do not want a fire in the ceiling caused by wires heated up or the fixture shorting out. Buy a different light kit for the fan that calls for 60 watt bulbs or buy a desk lamp or stand up lamp for extra light.

Are the sockets rated for 40 watts max, or 60?

Can you use compact fluorescents or does it have a dimmer? Is it a remote fan?

Frequently asked ceiling fan questions - Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-faq.php#19)