Can I use brushes and textures from free websites like brusheezy and unsplash to create photoshop actions and put the used brushes in the main file?
Unlikely - it would require them to have commercial redistribution licensing which is not common even for free items
So should I create all the textures and brushes by myself?
It would definitely be better that way. Then you are not risking any issues
I should add that for Unsplash specifically, their license info is pretty clear and can be found here.
From what I understand from this, I can use their textures in my photoshop actions without a problem, right?