In The Old Man and the Sea, Hemingway puts Santiago in a position of adversity from beginning to end. He is old, he is not as strong as he once was, he is unlucky, and he is alone. All of these are counterbalanced by Santiago's ability to persevere despite all obstacles. The three people you mention all demonstrate that perseverance--the one quality which Santiago has.
DiMaggio was a great baseball player, one whom Santiago admired for several reasons. One of them was that he played successfully despite the adversity of a bone spur. Santiago drew strength from the fact that if DiMaggio could do it, he could do it.
The incident with the Negro is a reminder to Santiago that he has persevered in the past and he can do so again. He once conquered his adversary and his own weakness to win a match of strength--a necessary reminder as he battle his brother, the fish.
Manolin is a bit different, in that Santiago had to learn patience in order to teach the young boy how to be an expert fisherman. That same patience is needed as he brings in this fish by himself.
Santiago draws on these things in order to remind himself he can persevere despite all the obvious obstacles.