Language
Singapore has four official languages: Chinese, Malay, Tamil and English. Therefore, I did not experience any difficulties language wise. Elderly sometimes only speak Chinese, but people are very helpful when it comes to translating. I did not take a language course in advance.
However, something I had to get used to was the so called "Singlish" - a mixture of English, Mandarin, Tamil, Hokkien, Malay and many more languages. Also when Singaporeans speak English, they have their own accent which takes time to get used to. After some time, I discovered that Singlish is actually a very efficient language after all. Once I asked my lab supervisor if I can leave the lab a bit earlier. Instead of answering something like "Oh, no problem at all!" or "That's fine!" she simply said "Can!" which took me a while to understand. Over the time i got to learn a lot of Singlish which was quite fun and turned into a "tandem" with one of my friends - I taught her German and in turn she taught me Singlish. So do not be afraid to ask if you did not understand something!
Culture
Culture wise, I did not expect to spot such a difference to be honest. But I realised very quick that I suddenly did not belong to the majority anymore in terms of looks - people with pale skin, blonde hair and blue eyes are nothing too special in Sweden. However, in Singapore people might stare at you - especially if you suddenly happen to appear in a very "rural" area (the so called "heartlands") far away from any tourist attractions and "expat" quarters and if you hand out with locals. However, I would encourage you to get in touch with your classmates.
Fortunately, I got in contact with a german teacher at NUS who wanted to introduce me to her class that was currently preparing for their exchange to Germany.
I was able to experience some great moments with my singaporean friends in Singapore but also in Stockholm and Germany!
Another thing which I experienced is that Singaporeans study A LOT! This however has different reasons: First of all, they have to pay fees each semester. Second, people take up scholarships (to cover for the fees) but the companies normally have requirements like a certain average each semester. Third: The bellcurve. Meaning, if you score 80points on an exam but your classmates all scored 100, you'll fail. But don't worry since the Bachelor of Honours courses normally do not have the bellcurve system. So do not judge but maybe try it yourself.
Culture Clash
If you want to go out with some exchange buddies, a night normally looks like this: You meet up after dinner to go for some beers and you eventually end up in a club and drink some more. However, Singaporeans are different: You meet up for dinner or lunch or supper (yes, there is a fourth meal in Singapore normally eaten around 10-11pm) but normally you do not drink. (Another advice at this point: Practice your chopstick skills a bit before you go!) Also, when I wanted to hug some of my friends for goodbye, I realised they don't do that usually so mostly it ended up in a very awkward hug in a way!
I really enjoyed spotting all those cultural differences during my time in Singapore and also embraced them!
Also a part of the Singaporean culture is food. The food is so cheap (but of a good quality!) that most of the families go out to eat instead of cooking at home which is (how I felt it) sometimes even more expensive.
You have to be brave and curious sometimes and just order things. I happened to try a lot of things - from the famous stinky fruit Durian to thousand year old eggs, chicken feet, BBQ stingray... (definitely recommend the last one!) But if you are more a fried rice kind of person, that's also no problem. However, after some time I started to miss things like bread or a fresh salad.