A smirk is a smile that is smug and slightly offensive. People often smirk at you when they think they know better than you do.
Someone is smug if they are very confident of their ability to do something, but at the same time are calm and complacent about it, as if they can do it very easily.
You are sorry when you have done something that makes you feel bad. You say you are sorry by apologising.
You are tired when you are sleepy and need to go to bed, or when you have worked really hard and are exhausted and worn out. The little boy in the picture is very tired.