HAVING FUN and SWINGING are the correct answers for this question.

1. In a poem swimming in the forest would be fine, on a quiz swimming needs to be in the water.
2. If the man in the picture were Tarzan in a loincloth then yes, he could be going to work.
But it is not Tarzan. It is just me.
3. I am HAVING FUN. 
4. I am SWINGING on a vine. SWINGING is not a word people use very often, so you may not know that particular word. HAVING FUN is an easier way to say it.

1 They are BALANCING spoons on their noses. You might not know the word BALANCING, but you should be able to understand from the context that BALANCING is what is happening with the spoons and noses.

2 No.

3 They might be at a cafe and they might have been eating ice cream, but that is not what we can see in the picture.

4 They are not on a train, so this cannot be the correct answer. Unless. You challenge me with your excellent knowledge of English idioms. You will get an A for effort, credit for explaining your answer choice, and mayeb even some ice cream. For fun.

1. The lyrics of the song are quite specific "I don't want to be a chicken"
2. Convince me; this could be a TPR lesson in flap, shake, or dance.
   
3. This is the truth. Everybody wants to do the Chicken Dance.
4. If conferences were fun like this then yes. But conferences are ...