"Arwa has a new cat."
Translation:عِنْد أَرْوى قِطّة جَديدة.
قِط (Qit^). Just by removing the ta-marbuta at the end (i.e. ـة) the word would turn into masculine.
This said, there is also another word for cat in Arabic: Hirr (هِر) and Hirrah (هِرّة) (masculine and feminine respectively). I remember some of my teachers saying that these two are more commonly used in the Arabic of Yemen (not the dialect nowadays but the Arabic of ancient times in that region).
Aand (to have) comes from Egyptian Arabic, right? Normally it doesn't exist in MSA?
No it is pure Arabic. However, the usage here is somewhat "egyptian" in style if I can call it so.
Generally speaking it means "at" and it is used to mean "to have something". There is one word also you might encounter which is not used in dialects in a common way, which is لدى (ladá). The last letter is not Ya', it's Alif maqssúrah (it has no dots and it is spelled like Alif).
Some scholars point out that there is a difference between the usage of the two words: عند and لدى. It is said that عند is used when someone has something in general, while لدى is used when someone has something at the moment of speaking.
All in all, it is OK to use it I guess - at this level.