Hi Amaraj! Julianne from Mixpanel Support here. Diving right in:
1. I'd recommend using the Profile Activity API to export the user activity. This API will return the activity feed for the specified users. Note, you will need to transform it to be in CSV format.
There isn't a direct way to export the entire activity feed in the UI. However, one option there would be to generate an Insight report showing the events for the specific user, along with breakdowns on the properties that you're interested in. You could then export that report as a CSV.
2. There also isn't a direct way to export the entire activity feed for all users within a cohort. At a high level, to do this, you could export the cohort users (ie via a webhook), and then export the data for those users via the Raw Export API or Profile Activity API. Note, there are rate limits for the APIs documented here.
Is there a specific question you're trying to answer with the exported data? It may be easier to analyze the users in Mixpanel rather than trying to export the raw data.
You definitely do both via the Events tab. However, I'm sure there's a limit to how much data you can download at once. So, you'll have to look at that once.
Amaraj J.