My personal interpretation
Her ex-boyfriend explained that if it killed her it would then work it's way back through the line. However, he got targeted after a one night stand so how did he know this? How does anyone know it would keep going all the way back to patient zero, if had ever done this then wouldn't everyone involved be dead?
Hugh / Jeff has a one night stand with some random lady at the bar and he starts seeing them. Although, he doesn't see them after having intercourse with his girlfriend (Annie), the very same girl who dies at the beginning of the movie.
The reason for him to go to a different place and starts dating Jay is unknown, may be his girlfriend starts seeing them and he decided to stay away from her and the place until everything settles down, came to a different place and started dating Jay.
Guessing game at the theater, a pivotal scene where Hugh points at some girl but Jay can't see her, it again started following him at the theater and at the restaurant. Meaning, the previous night Annie (his ex) died (starting scene) and it started following him. This is where he formed the theory that he could pass it to someone else by intercourse and it comes back if the person, who's been passed dies.
Is it explained why, rather than waste time seducing Jay, he didn't just take a trip to Brazil or somewhere far away and sleep with a prostitute?
(continuation) Now he has to pass it to someone else to keep himself safe, so, he passes it to Jay. (Please don't be mad, I know he could have done the same thing to some random prostitute but may be he thought it's not safe to do it with a prostitute without condom :). Also he suggests Jay in the later scene to pass it on by sleeping also tells that it's easy for her, she's a girl and anyone would sleep with her.).
Was the girl from the opening scene the girl in the picture with him?
Yes, it's the same brunette, it's the only connection (in the entire movie) between the girl in the opening scene and the one in the picture.
Intercourse with 3 men on a boat, What was the actual point of the scene?
After that scene, when Paul meets her, she says, "It's gonna be here sooner or later.". She had intercourse with the three guys on the boat and while returning home she cries because knowingly she passed it on to innocent guys.