Hezký as nice is acceptable for inanimate objects. House, car, shoes...
But when you say NICE about people in English you are talking about their inner beauty. About them being good pleasant people. Nothing to do with a shape of their nose or other features. HEZKÝ though only talks about what things look like. She can be pretty (hezká) but a completely nasty person.
Czech doesn't have a palatalization system. There are no palatalized and non-palatalized consonants in Czech. This old Slavic system evolved a long time ago into a simple distinction between palatal/post-alveolar consonants and other (usually alveloar) consonants. So "s" is always /s/ (never palatalized), and "š" is always /š/ (post-alveolar, still never palatalized), or "t" is /t/ (alveolar) and "ť" is (IPA: /c/) the palatal "version" of /t/, but not palatalized.