to split one’s side/ clench

Would you tell me whether I am right about my interpretation of the expressions in bold in the following sentences?

He laughed until his sides were splitting and the bottle of cheap whiskey he held clenched in his hands slopped on the floor.

I laughed till I thought I should split one’s side.

to split one’s side = laugh one’s head off. Be extremely amused, laugh uproariously ( (this one is clear already)

He clenched his hands into hard fists.

He clenched the arms of his chair

clench = hold in a tight grasp; squeeze together tightly

Thanks for your efforts.