Yes. The Bible says God is not willing that any should perish. What could a baby do that would be considered as a sin? At some point though, we become old enough to discern right from wrong and our deviations from God's will (sin) are held against us. All people will sin -- we all fall short of God's glory.
Yes.
Is that your final answer? Humans are entitled to Heaven? If only we didn't sin, God would have to let us into Heaven? Entitled?
We are not even entitled to life on earth, even that is an inestimable gift from God. To say that we have an entitlement to Heaven, to eternal life with God is astounding.
SD