The answer to your question is really that the entire story is written in the stream of consciousness technique. There is no reasoning why the speaker's thoughts drift where they do. We are simply taken along for the ride. Also, in regard to the specifics of your question, those two things that you mention are true allusions, both of them to visual types of art.
The first allusion is to a famous cartoon character named Porky Pig. As a character, this poor pig stutters and is never quite sure of himself.
Neither is Professor Kohler. "In a pig's eye" is a common (old) expression meaning "it will never happen." The professor saying this as he refers to Porky Pig is probably a reference to his own weight issues. In addition, it's also a reference to the kind of relationship, the kind of positive relationship, that he could never have.
The second allusion is to a famous piece of art called "A Lass and a Lack," which shows a man and a woman on a date at a restaurant, with a waiter looking over them. It is obvious that the girl is the lass and the boy has the lack. It definitely shows the man striking up a sweat because he doesn't have enough money to pay for the dinner. The waiter notices, and looks at him with disgust. It implies that he is the man in the picture, and the girl is the woman from the picture. He definitely has a lack of many things. She, in her youth, has no lack at all.
In conclusion, I also want to mention that the "date with a lover" that you mention is not really a date at all. It is really just a sexual encounter with one of his students. The two allusions we speak about are really just part of the result of that encounter. Finally, remember that the true reasoning behind all of this is that the author wrote the entire story in stream of consciousness technique.