While Covid has continued to improve over the last few months, there still are entry requirements when you fly into Spain and when you fly back to the US
To enter Spain you must show either: - a vaccination certificate (last dose must be no older than 270 days), - a negative diagnostic test (performed within 72 hours prior to departure for PCR or 24 hours for rapid antigen test), or - a recovery certificate (provided more than 11 days have elapsed since the first positive NAAT or RAT was performed, and this recovery shall be valid for 180 days thereafter) Note that these requirements are as of 4/24 and may change at any time - for the most updated info, visit: https://www.spth.gob.es/home Additionally, a few days before traveling, you will have to fill in the following form to obtain a QR code that the Spanish authorities will ask for when you land: https://www.spth.gob.es/ If you prefer so, you can also download the app and fill in the form on your phone
You will need to get a COVID-19 viral test, PCR or rapid antigen, (regardless of vaccination status or citizenship) no more than 1 day before you travel back to the United States. You must show your negative result to the airline before you board your flight. There are plenty of testing centers where you can get a rapid test, even on a Sunday. For instance, https://cerba.com/en/home/ (with a few locations in the city) allows you to book your testing time in advance. Additionally, you can also get tested in the BCN airport (T1): https://flycovidtestcenter.com/en/barcelona-t1/ (booking an appointment in advance is also encouraged)
No, if you are visiting other European countries, please check their requirements as these will vary across countries