Is there any way to estimate an average amount of transactions per user per month? I would like to get a general picture about Bitcoin ecosystem development and dynamic changes, based on some numbers. Is it possible to have an estimate of a number of active users somehow? Preferably, based on the data from blockchain itself. Is it possible to estimate an average amount of transactions per user per month?
While it is not possible to know the exact amount of users, there are still ways to estimate it by making assumptions and looking at online polls to utilize the wisdom of the crowd.

currently, my estimate is somewhere between 80 and 100 million users, although that refers to unique individuals who has ever used bitcoin, rather than unique individuals who are actively using it today.

furthermore, it is impossible to correlate transaction counts to this number as some services and systems generate automated transactions.

the other answe suggest that you look at bitcoin days destroyed, which is a measure for how long tokens have been stored sonce last transferred.

you could use that if you correlate it to other data sets, but beware that the time between broadcasted transaction and being mined in a block is unaccounted for.