Can you say "la" or "msh" instead of laysa?
It depends on the accent you're speaking this is "Fusha". Usually in arab country the language changes for example in Iraq they "ma" (Ex: ma 3indik bayt).
Hope this answers
Isn't it: ليست عنده جودي وشاح حديد. Because Judy is a female person?
It would be just عندها without جودي, because عندها already has the "she" in the word. You can't say "Judy she doesn't have a new scarf".
عندها :I mean