If we’re talking about a true conversion, then yes, it is.
Yes. The bible says in Romans 8: “16 The Spirit himself testifies with our spirit that we are God’s children. 17 Now if we are children, then we are heirs—heirs of God and co-heirs with Christ, if indeed we share in his sufferings in order that we may also share in his glory.
The Spirit deals with us, and the inner us knows it.
Also, Jesus said in Mt 7: “16 By their fruit you will recognize them. Do people pick grapes from thornbushes, or figs from thistles?”