pixie/tongtong/krystle,
Don't feel bad lah. We are all doing our best that we can. We are all great mum, k!
For throwing tantrum, trust me, it soon will pass, very soon! HR's one lasted like 2 months or so, and he never had any (major one, minor ones cannot avoid lah) since then. I know we all have very different parenting style, but in my opinion and what I have gone through, kids this age don't really need disciplining. What they really need are love, attention and trust, it gonna work both ways. Once he is sure that he is so important to you and that you trust him, and he can trust you, he will change his behaviour in no time. And it's also about confident. It's very important to help kids build up thier confident level.
About learning. I am an advocate of learning through play, and it works well for us. Whenever possible, I do things and I play together with them, positioned myself as a kid

And create the environment for them. For example, now that HR is so hooked on colouring, we brought him to choose the colouring book that he likes, and bought a new set of colouring pencils and a train sharpener for him. Give him lots and lots of praises. He has like almost 10 colouring books now and all within easy reach for him.
Don't think too much and too far away, appreciate the very moment now, 活在当下, appreaciate who he is and love who he is!
Be positive, be positive, be positive!!!