Contacts and Email seems to be the easy part: you can download the emails via IMAP to a client like Thunderbird, and the re-upload them on a new account. Years ago I did this transferring from one G Suite account to another for a friend, worked very well. Contacts can be exported in CSV and then imported bia CSV, no big deal too. I have routinely transferred loads of contacts between different systems this way, including Gmail. With calendar, I never had a necessity to transfer data, but I imagine that there are ways, given that it uses a standard iCalendar format.