Q. Can Satan do anything that God does not permit, (example, Satan asking God to remove the hedge he had around Job, and God limiting Satan’s actions against Job)?
A. It’s more a case of God being forced to remove His protection because of our sin. Satan can’t make Him lower our hedges arbitrarily. But if we’ve sinned and fail to confess, he can’t refuse if Satan asks for some kind of access to us (Luke 22:31). Remember, Job’s self-righteousness was a sin that left him vulnerable, even though God said there was no one like him on Earth.
When we sin and don’t confess, God has to lower our defenses for two reasons. First He can’t be in the presence of sin, and second he wants us to confess and if we refuse, He will permit Satan to help make that happen, subject to His limitations.
As soon as we confess, we’re forgiven, and purified from all unrighteousness. (1 John 1:9) The hedges go back up and we’re protected again. Later, God will often find a way to turn Satan’s mischief against us into a blessing.
We’re saved for all eternity, but on Earth we’re aliens behind enemy lines and need God’s protection to avoid being singled out for torment. Seeking forgiveness every time we sin makes that possible.