Good questions! I’ve actually wondered them myself, and am about to post a related question…
If you will be residing in another city, you might want to check the following website to find the email address for that city. I say this because, well, you might get different answers depending on who/where you contact.
I don’t know the answer to questions #1 and 3 (my residency started in January, so I had the luxury of just assuming a Calendar year applied). As for #2, I believe you can travel back and forth, provided that you meet the minimum 182-days requirement. At least that was acceptable in my case (also a US citizen). Please note that: 1) In Spain, they stamp your passport when you enter AND when you leave the country (unlike in the US, where passports are only stamped upon entry), and 2) they will ask for a copy of your entire passport (i.e. all pages) when you renew. Each time I submitted my renewal application, I also listed the range of dates that I was in/out of Spain, and circled the stamps that corresponded those dates in the copy of my passport that I submitted with my application. I figured they’d appreciate the full disclosure and that I had cut out that work for them.
Hope this helps! Good luck!