How can one determine approximately what percentage of options trades are buyer-initiated vs. seller-initiated? What measures of order flow are available specifically for options, preferably for individual contracts covering specific strikes and maturities?
Pan and Poteshman (2006) were able to obtain a "unique dataset from the Chicago Board Options Exchange (CBOE) which breaks down the daily trading volume of both call and put options into four categories according to whether a trade is initiated by a buyer or a seller, and whether the initiator opens a new option position or closes an existing option position." I don't know where they got the data, but obviously this would answer your question.
Otherwise, you could use the Lee and Ready (1991) algorithm to infer, with some noise, whether a trade is buyer or seller initiated. In fact, Amin and Lee (1997) did precisely this in a paper studying options trading around earnings announcements.
For every option bought there is an equal quantity of options sold.
For example, when reporters say "stocks dropped because of heavy selling", this is strictly speaking impossible. For every stock sold someone is on the other side of the trade -- so stocks dropped because of heavy buying as well with equal intensity. What is happening is that the willingess to pay for stock (demand curve) has shifted to the left, therefore prices have dropped.