On "delivered" vs. "saved" - in the Joel text and many others it is much simpler. The Hebrew is delivered and the Septuagint is saved and of course Peter quotes the Septuagint. Often "delivered" is translated "saved" though the OT context may be a military situation.
And as to calling on the Lord, of course this is a "pregnant" phrase that includes 1)conviction of sin - not just wanting help -2)faith in Jesus' person and work as alone sufficient to justify; and then as you wrote, 3)a continual calling on him in trust for the necessary strength and holiness to live as a true regenerated Christian.
Carry on, brother!