In addition to the -ku suffix (which MarcusWhel1 pointed out), there are other suffixes denoting possession. Here's a complete list:
-ku = my (from "aku")
-mu = your (from "kamu")
-nya = his/her (from "ia")
I think that might be "besaraku" or do they shorten it? "Aku" is another word which is informal for I, while "Saya" is the formal version.
https://www.duolingo.com/skill/id/Basics-2/tips-and-notes You may need to click on Basics-2 skill and click on the lightbulb for the Tips and notes on the web version of Duolingo.
No, the possessive pronoun comes after the noun. "Kucing saya besar" = "my cat is big". "Saya kucing besar" = "I am a big cat".