English is the official language of Gibraltar but many people also speak Spanish and the local language, which is called Llanito and has a mix of Mediterranean words in it.
Tips for restaurant service in Gibraltar is typically around 10%, so if you are in a more informal restaurant that has a service charge, just round up to the closest £5 and that will be sufficient.
The Gibraltar-Spain border is a busy external Schengen Border and Gibraltar is outside the Customs Union. There are rules on taking food and drink into the EU, which apply when crossing the border from Gibraltar to Spain . See the Spain travel advice page for details: https://www.gov.uk/foreign-travel-advice/spain/entry-requirements
Gibraltar uses the pound sterling. Whether it is issued in the UK or Gibraltar doesn't matter.
The taxi rank is located immediately outside the main terminal building at Gibraltar International Airport. There are also ranks in town at Casemates Square, the Anglican Cathedral and Trafalgar Cemetery, and a 24-hour radio taxi service is available. Tel: + 350 200 70027 for 24hr radio service.
Currently, U.S. citizens can freely enter the Schengen Zone (an area of 26 countries covering much of Europe) for up to 90 days for business and/or tourism purposes. End of 2023, all U.S. citizens traveling to the 26 Schengen Zone countries will need to register with ETIAS or will risk being denied entry.