Will I need to go through extra security when flying from one Schengen country, to another, and then to the United States?

Since you will leave the Schengen area at Amsterdam, you will need to go through EU exit immigration there. Since your flight is headed to the US, you may also be asked some "security questions" at the gate and potentially have your carry-on bags briefly inspected. However, you should not need to go through an additional full security inspection (X-rays etc).

Yes. Schiphol airport has a "Schengen" and a "non-Schengen" zone. To move from one area to another you have go through security and passport control (passport control happens if you enter/leave the Schengen zone, not if you travel between countries in the Schengen zone (assuming no temporary measures)). You do not have to go land-side, you can move between the zones air-side.

On top of that, there will be a short interview for all passengers flying to the USA. For many flights, this happens at gate D1 (your boarding pass will say D1 as your boarding gate -- you'll be redirected to the appropriate gate after the interview). There is an exception for passengers flying Delta and starting their journey in Amsterdam -- for them, the interview happens right before the security check. But that does not apply to you. I once has the "pleasure" of being interviewed at gate D1 and almost missed my flight because of the long queues. But that was years ago, and shortly after they implemented the "interview everyone at the same place" (before that, the interviews happened at the gates). Since, I've either flew Delta, or via a London airport, so I've no recent experience with the mass interviewing, but I think the process is much smoother now.