I believe that the God of the Bible is a just God. And we as humans are inherent sinners. We can do nothing to reconcile ourselves with our creator. Therefore, in is absolute justness, God cannot allow us into eternal paradise, heaven. In order to atone for the sins of humans and create a new covenant between God and His creation, Jesus Christ was sent to die and be resurrected as the Messiah. And only through him can we come to the Father.
With that said, I want to address your last sentence. God has an absolute hatred for our sin, but He loved us so much that He made a way for us to be reconciled to Him so that we could once again be in communion with Him through the Son.
Yes, I do believe that salvation comes by grace alone through faith in Jesus Christ alone.
In John 14:6 Jesus says "I am the way, the truth and the life. No one comes to the Father except through me."