What do trees do when the wind blows? Swing or rock?
Are the trees swinging?
Are the trees rocking?
The wind is rocking/swinging the trees.
The trees are rocking because of the (high) wind.

Or both verbs can be used? Are the sentences above correct?
What about grass?
The grass is swinging/rocking in the wind.

Question

What do trees do when the wind blows? Swing or rock?
Are the trees swinging?
Are the trees rocking?
The wind is rocking/swinging the trees.
The trees are rocking because of the (high) wind.

Or both verbs can be used? Are the sentences above correct?
What about grass?
The grass is swinging/rocking in the wind.

Answer

You would tend to say the trees/grass are 'blowing' in the wind. Rocking you wouldn't use, that word is more for objects such as 'rocking chairs' and isn't used much. Swinging is used more for animals e.g. 'the monkey is swinging from branch to branch/tree to tree'. Hope that helps!

Answer

1) Sway or swing would be the common verbs. 
I've asked the similar question and got the excellent explanations which might be helpful for you https://www.italki.com/question/394363

2) Grass usually 'is swaying in the wind' or 'swinging in the wind'...  It also 'swishing in the wind' but it's about sound, not about movement. As for the 'rock', the wind can rock the grass, but I've never encountered the expression "grass rocking in the wind'

Answer

Not exactly the trees, but its leaves and branches will move, swing, shake, move or whatever you like.

Answer

I would say "The trees SWAYED in the wind."