This app was mentioned in 3 comments, with an average of 1.67 upvotes
Do at least one hike. Go to Piscinas do Porto Moniz, to Balc玫es (sightseeing place), see sunrise in Pico Ruivo, stay until 20pm at the beach and see the sunset, also, before you go, drink all the ponchas you can, it will make the trip back much memorable. Also don't forget to calmly walk in the city center and try to feel the locals personality whether in Mercado or just walking, normally they are nice people馃憤 Don't adventure yourself outside of the recommended hike paths and estimate the time when you start. Hikes it can be dangerous, use a local guide or download https://play.google.com/store/apps/details?id=com.walkme There is a lot more you can do, but this what I thought for a start.
there's an app called WalkMe Levadas Madeira
Its great
https://play.google.com/store/apps/details?id=com.walkme&hl=en_GB
There's another version for iphone I believe.
I'd recommend renting a car with a gps to get around
sorry I cant answer your questions but I thought this info would be useful -
I know there's an app that you should get
https://play.google.com/store/apps/details?id=com.walkme&hl=en