does satan have legal claim over a non believer, ?
Your authority is inherent to who you are in Christ. When you were adopted into God's family, it's like being taken in by the wealthiest, most powerful person that exists. As a believer, you receive the Holy Spirit, and Satan and his army of devils and wicked spirits are absolutely terrified you'll find out who you are in Him.
Satan's army are pressed into service and they hate each other. The "higher ups" in the army of darkness, punish the lower devils for not making their assignments. Failure and all expressions of godly dominion, remind them of their defeated position and certain expectation of eternal judgment.
They move in desperation from fear of retaliation from their own and from the force of God moving in resurrection power.
For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places.
Eph 6:12
Even a baby Christian has more authority than all the devils in Hell. They'll work hard to keep you from finding out about it, because that would only cause more problems and a greater fear.
Non believers haven't been delivered from the power of darkness, so as well meaning as they can be, their whole lives are subject to the rule of darkness and fear. (Many don't know the depth of the fear because the enemy lets many of them continue their harmless, godless lives, quietly going off to Hell in a basket.
Giving thanks unto the Father, which hath made us meet to be partakers of the inheritance of the saints in light:
Who hath delivered us from the power of darkness, and hath translated us into the kingdom of his dear Son:
Col 1:12-13
Again, the devil taketh him up into an exceeding high mountain, and sheweth him
all the kingdoms of the world, and the glory of them; And saith unto him, All these things will I give thee, if thou wilt fall down and worship me.
Matt 4:8-9
The devil has been running things here since Adam's fall. He had the authority given to him by the servants of sin (Satan).
Everything is "fathered' and Satan is the father of the nature of all lies.
Jesus answered them,
Verily, verily, I say unto you, Whosoever committeth sin is the servant of sin. And the servant abideth not in the house for ever: but the Son abideth ever.
If the Son therefore shall make you free, ye shall be free indeed.
John 8:34-36
Many believers still walk in fear and allow sin to have dominion over them, often through ignorance, or because the believer still loves some sin in their life, thus giving him access to afflict him.
Jesus spoiled the principalities and power and took the keys of Hell and death. Satan's dominion is no more, and his power broken, but God's dominion must be enforced on this earth.
Unbelievers must turn to Jesus and be "translated" into the light of God's kingdom. Even if believers turn to sin, they need only repent and walk in the light and God stands behind them as they take up God's Word in His authority and run him off!
Until they change kingdoms, Satan has some measure of authority to afflict them. They would kill us all outirght, but they are only given some space to do what they do, somewhat based on ignorance and willful behavior. God allows blessing and cursing. It's all based on the authority of God's Word. The devil knows it well, except where it concerns him in the end (denying the reality of it). When you sin in an area, many will try to get God's permission to afflict you (often wanting to sift you as wheat).
it's important for us to pray for our unsaved family members, because their lives are dominated by the forces of darkness, and our prayers dramatically cause God to intervene on their behalf.
Part of knowing that authority is walking in it, the knowledge of the truth setting us (and others) free.