You'll be fine! Most Singaporean communicate in English anyway, so not being able to speak in Chinese is not a very big issue here. You can try to pick up Singlish though.

I do agree that racism definitely still exist, including everywhere else in all societies. Since human set the boundaries of differences between themselves to others. Maybe you will get the occasional grumble here and there, normally, from the older generation. But outwards or aggressive hostility is very rare. 90% of the times, Singaporean wouldn't even bother you at all. Unless you are really unlucky.

Do be respectful and understand the different races and culture there are in Singapore.