No conditions. Come as you are (Jn 3:16).
Yes, believe. Tell your household and they will be saved, too (Ac 16:31).
That’s right. If you are his, it will show by good works. If you remain of the devil, those evil works will eventually be known, as well.
Now the works of the flesh are evident, which are: adultery, fornication, uncleanness, lewdness, idolatry, sorcery, hatred, contentions, jealousies, outbursts of wrath, selfish ambitions, dissensions, heresies, envy, murders, drunkenness, revelries, and the like; of which I tell you beforehand, just as I also told you in time past, that those who practice such things will not inherit the kingdom of God. But the fruit of the Spirit is love, joy, peace, longsuffering, kindness, goodness, faithfulness, gentleness, self-control. Against such there is no law (Ga 5:19–23).