Yes, uber works in Taiwan and is quite affordable. We recommend it if you cannot speak mandarin, as it eliminates any confusion regarding destinations. Yellow cabs are relatively inexpensive, and can be hailed curbside - look for a red light in the front windshield (vacant) - prepare your location in google maps to show the driver if you cant speak mandarin.
Chunghwa mobile and Taiwan Mobile are the dominant carriers, and both are sold in the airport. They are quite affordable for short stays and unlimited data, so eSIMS arent necessary unless you want instant connectivity.
Apple pay works in most convenience stores, fast food and restaurants (not street food), but best to keep some local currency in case.
Google maps is widely used here and reliable. Use Google Translate with Chinese (traditional) if you need to ask someone or show them something.
The subway is clean, safe, fast and English friendly. I prefer to use it during rush hour, as traffic can be bad around rush hour. You can purchase a subway card in any station with a $100ntd deposit. You may use the Go! Taipei Metro app to navigate (google maps also incorporates the MRT into their options for getting around.
No, almost all services here do not require tips of any sort. If you are happy with service, please feel free to tip.