Yes, at this age small children are just beginning to develop the linguistic skills in their on native language. This is what you should bear in mind when teaching them some English in addition. Normally, at that age it works without any problems and without the mechanisms that make foreign language acquisition more "difficult" at a later stage because the way how languages are learned is changing.

You have said it yourself - singing and other language games are fine at this age, and the emphasis is on games. You should change your game activities regularly and add some new to them on a regular basis, because after a time with all the same stuff, children will get tired of it and lose concentration and perhaps also interest in that area.

Good luck!