I think this can also be translated as "There are stars in the sky".
I can say Aakash instead of Aasman, right?
Yes, they are synonyms.
Yes you can
"Stars are in the sky" would more like तारे आसमान में हैं
What's the difference between सितारा and तारा?
None. They are synonyms. The only difference is that सितारा is a loanword from Persian and तारा is a native word from Sanskrit.