Yes, definitely ensure you choose candles SPECIFICALLY designed for use in wax play (Eg: Avoid beeswax, it melts at a much higher temperature. go for paraffin, basically, low melting point candles) Do some research on that beforehand. As for dripping the wax onto sensitive parts, yes you can do, but it is going to hurt more than less sensitive areas, obviously. I have never been quite brave enough to allow wax dripping onto my clit, but I have had it on my vaginal lips and nipples and my partner has had it on his penis and balls, without any problems...hurts a LOT though. Start with the candle reeeeeally high, this way it will be cooler when the wax hits. You can lower it gradually until you find your partners limits.
What does it feel like? A little like hot or scalding (Depending on how high you hold the candle) water hitting your skin....an intense burning for a split second, then the wax cools and dries almost instantly...the skin can feel sensitive afterwards too.