Did Severus Love Harry?

Snape's tears at the end of the book/movie don't mean that Severus Snape ever loved Harry Potter. Harry's mother was Severus' great unrequited love, and that was the only reason for his emotional attachment to the little future wizard.

Why did Snape care for Harry?

“After all this time?” “Always,” said Snape.” Snape's 'him' is italicized, and then he produces a Patronus the same of Lily Potter's. This indicated that Snape cared for Lily, and cared for Harry because Lily would have wanted it.

Why did Snape treat Harry so badly?

He portrayed himself as aligned with the dark side because that was his job as a spy. He had years to ingratiate himself with them, even becoming Draco Malfoy's godfather. So in summary, Snape is so angry with Harry in particular because he is petty in a sense; punishing the son for the sins of a father he never knew.