When you get an e-visa online, what documentation do you get? Is it something that goes in your passport or a separate paper?
The visa in a paper document you print out at home: https://www.evisa.gov.tr/en/info/what-is-e-visa/
What is the advantage to the e-visa as opposed to getting a visa at the Istanbul airport? My passport is nearly full. Would this eliminate a need to have a visa stamp attached to my passport page?
When you land at Attaturk, you can go directly to passport control if you have an e-visa. If you don't, you go off to the side in a line (sometimes long, depending on the day and time) and get the printed e-visa, and then rejoin everyone else. We were able to just plod on through, and were happy to do so after a long flight.
But if you get the visa at the airport, you get a lovely stamp ;-) !