If you visit Singapore and would like to buy some gift, you may get it at Kampoong Bugis, Chinatown or in Mustafa Center. Except in Mustafa Center, you may bargain the price. So you can save your money :) Unless you have a lot of money to spend :D .
I would say bring your light clothes as Singapore is known for its humid weather. It takes about a few days to tour around the city/attraction places. Shopping malls are everywhere. Hopefully to see you here when your visiting the city.
Is it safe to visit and travel Singapore for 2 girls together without any family member or any boys?
Very nice country. Clean and Discipline people that includes the tourist (or you pay the corresponding fine). A lot of theme park for the entire family or for couples. Different hotels from average to 5 star. Cab driver are nice and very accomodating.
I'm visiting Singapore early next year. Is there anything you can suggest I should see, do or try to eat?
Avoid travelling at peak hours (8am - 10am and 6pm - 7:30pm) via MRT. It gets super crowded and you might not board the train even after missing 3 trains. However, should you need to still travel, the good news is, Singapore MRT train frequency is about every 3 - 6 mins. The bad news is, you will be squeezing flesh to flesh with the crowd.