Hey, don't get mad. It's an innovation. Not everyone knows it yet, and not everyone likes it. Nothing is wrong with me other than having been exposed to the word once, and it stuck with me ever since. Here, it has entries on the Wiktionary and the Oxford dictionary: https://en.wiktionary.org/wiki/ze#English https://www.lexico.com/definition/ze
Have a good one!
Questions in English employ reverse word order, meaning that the question word or the interrogative phrase must be followed by a verb. You can't ask "What kind of cat she has?" for the same reason you can't ask "What your name is?". You can, however, ask "What kind of cat has she?", although it sounds rather old-fashioned. The word order in your sentence would work as a sub-ordinate clause though. For example, "I asked her what kind of cat she has." :)
'Hänellä on' is a construction that translates to 'he/she has'. It is 'hän' (he/she) + the suffix '-llä' which literally would be 'on him/her'. Hän can be substituted by any other person/subject, but the verb ('on') stays the same, so third person singular: Minulla on (I have), Liisalla on (Liisa has), isällä on (father has) etc.
Please also note that 'ä' and 'a' are two completely different letters in Finnish and using the one instead of the other can change the whole meaning of a word. 'Han' is not a Finnish word as far as I know, but for example 'sade' means 'rain' and 'säde' means 'ray' or 'beam' so you can't always assume people will understand you just left off the umlaut.