Is historical information on the counts of trades in single stocks, futures, options etc. available somewhere for download or purchase? If not, which ways can you think of to gather it?
Its not available for free anywhere that I know of. Your only option is to purchase tick data for the instruments you're interested in and then count the ticks per trading session (or whichever timeframe you want to use).
EDIT: This link might be interesting for you regarding how to get market data.