Advice from a fellow student! :)
1. A few notes of an old tune were enough to summon up the memories of his childhood.
Nitpicks: "An old" tune? if it's enough to summon up memories, it should be a bit more specific, or if it was already specified in the last sentence, you should use "the old tune."
2. After remaining silent and contemplating for a while, he told her that their relationship was finished.
Nitpicks: If he remained silent and then tells her he was breaking up with her, then saying he or she was contemplating would be redundant. The reader is smart enough to know that they where either contemplating or thinking about a way to break the news.
"After a moment of silence, he told her the relationship was over." Or even, "After a moment of silence, he whispered, "It's over."
3. Running and shouting after the thieves, he did not notice that he was barefoot.
Nitpicks: It works, but it's a bit weird. Especially if this is all happening in the present tense. Try, "He abandoned his shoes and ran in pursuit of the thieves, screaming and shouting for attention." I guess it takes the whole oblivious part of it, but it gets the job done and ultimately accomplishes the mood you were trying to set when he said he was barefoot: he was so adamant and fast to try and capture them that he even forgot his shoes.