1. How quickly does 'Activity' reflect on account
2. Are there any are specific parts of the forum that you don't accumulate activity from by posting?
You must read
this to find the answer.
3. Is there an upgrade option (paid in BTC) to reach higher member status?
So far you can only pay for
copper membership with features equivalent to the "Member" rank. But it will not change your current rank.
Read more here