Madeira Trip Questions!

It’s my first time visiting Madeira mainly going for surfing and hiking (4-7 April) , I want to see:

• Funchal Old Town (Zona Velha)

• Pico do Arieiro • Pico Ruivo • Ponta de São Lourenço • Miradouro do Guindaste • Miradouro da Ponta do Rosto • Levada do Caldeirão Verde (PR9) • 25 Fontes & Risco Waterfall • Seixal Beach • Porto Moniz Natural Pools • Ribeira da Janela • Câmara de Lobos • Cabo Girão Skywalk • Santana Houses • Eira do Serrado • Curral das Freiras (Nun’s Valley) 

1) am I missing a hidden gem?

2) do I need to rent a car? or taxi is easy?

Thanks!