Kaunis is an example of the old Germanic loan words in Finnish. In Proto-Germanic it was "skauniz". Finns do not like consonant combinations in the beginning of the words, and therefore the first sound "s" has been dropped. Also, we do not have the voiced "z", so the last letter became a "s". The modern Germanic languages have in fact changed more, so it is not easy to recognize that "kaunis" is the same word as the German "schön", Swedish "skön", Danish "skøn" and Norwegian "skjønn" (and Dutch schoon = clean). As we can see, the diftong "au" has become "ö" in German and the Scandinavian languages.
"Hän" is indeed gender neutral, and therefore it can be both "he" and "she". However, it is not number neutral, and therefore "hän" cannot be "they". "They" is in Finnish "he". "They are beautiful and funny" is in Finnish "He ovat kauniita ja hauskoja". The words "kauniita" and "hauskoja" are in the plural partitive case. Partitive is a tricky thing in the Finnish grammar.
Beautiful and pretty both have their counterparts in Finnish. While beautiful (kaunis) can be assigned to almost any thing, pretty (nätti) tends to more often describe feminine things/phenomena. They can be used interchangeably without anyone batting an eye. Nice (mukava) and hauska (funny) are clearly separate, however :)