Tackiling the sin part
Highlighting a false premise, that one must experience something for one to know/understand it. It is worth noting that experience is a type of knowledge ...
This is actually quite a loaded question philosophically, theologically, etc. Theologically, there is always mystery.
13 if we are faithless, he remains faithful—
for he cannot deny himself.
Beginning here we see the reason. The mistake is to view sin as something, while it is actually an absence of something. cf. Evil | New Advent.
Jesus, is God, therefore, ALL Goodness, ALL Truth, ALL, Love, etc. Hence St. Paul, for he cannot deny himself.
Not only did Jesus not sin, he could not sin (he was impeccable cf. The Incarnation | New Advent).
Herein is the mystery: Jesus, as Son, moves naturally and necessarily toward the Father, yet also freely.
Sin understood here as doing one's will in opposition to God's.