Here is a question I might use to begin a Sabbath School lesson study discussion:

What problems did Jesus have and how did He handle them?

Which method do I think Christ used the most to overcome suffering?

Yes, He quoted the Scriptures, healed others and rubuked the hypocrisies in a kind way.

To say He offered a prayer to the Father though is like saying that boiling water is hot! A gross understatment.

Prayer is communication. He didn't offer prayers, He prayed almost constantly...a lesson for us.
To offer something is to hold it out and ask, would you like this?

Jesus prayed. Plain and simple.

Was Christ really rejected by His Father, or did He experience a temporary loss of faith?

A much smaller point, since Joseph was a craftsman in a predominently agrarian society, is it not possible that relatively speaking, Jesus' family was in humble circumstances, but still better off than some?

Imo His greatest suffering was during this temporary loss of faith.