Predestination ending scene

Yes, it's a paradox.

The entire point of the film, as the title suggests, it to play with paradoxes and predestination. A very detailed description of the film can be found on its wiki, but perhaps of more interest is the short story (just ten pages) on which it was based: All You Zombies, by the ever-wonderful Robert A. Heinlein. If you read its wiki, you get the same breakdown as Predestination, but written far more verbosely. To quote from its wiki:

'—All You Zombies—'" chronicles a young man (later revealed to be intersex) taken back in time and tricked into impregnating his younger, female self (before he underwent a sex change); he thus turns out to be the offspring of that union, with the paradoxical result that he is his own mother and father. As the story unfolds, all the major characters are revealed to be the same person, at different stages of her/his life.

It was this series of paradoxes which inspired the film's creators:

FLICKS: How did you first encounter the short story?
PETER SPIERIG: I had just been reading a lot of short stories and All You Zombies by Robert A Heinlein was just one that really stuck with me. I remember reading it and thinking ‘Wow, that’s a real original’. I gave it to my brother to read and he reacted the same way. We both thought it would be great to make into a film one day. We didn’t know how we were gonna do it, but we both thought ‘Boy, this would make an interesting film!’ And then eventually we stopped saying ‘One day’ and we said ‘Okay, today we’re going to try and turn this into a screenplay.’ That’s kind of where it all came from.

Wow, insane film this was. Here's a timeline diagram to help explain the events of the movie, looks like yes, he does eventually become the Fizzle bomber!

The agent/bartender, Jane/John, Fizzle Bomber, and the person Jane fell in love with is just one person.

My brain is bleeding.

I'm confused about his gender originally. He's a she... or she's a she, am I right?

I think it's more philosophical than confusing. Check this interesting read:- https://gravito.wordpress.com/2015/01/04/the-philosophy-predestination-is-trying-to-prove-timeline-and-predestination-paradox-lessons-spoiler-alert/

It is implied that the main hero is the Fizzle bomber but I think he couldn't have done the big bombing in 1975. When he killed himself, it was before the bombing happened. He told his older self that "his next bomb is going to kill thousands of innocent lives" and that he couldn't allow it. And then he shot him, before the bomb was even there.

Am I getting it right? And if the main hero didn't plant the bomb in 1975, who did?

The message of the movie is that everything that happens is meant to happen, and there is nothing anyone can do to change it: hence the title "Predestination". We all have a predetermined destiny that cannot be altered.

Essentially there is nothing John/Jane/barkeep/fizzle bomber can do to prevent his creation or transformation into the fizzle bomber. His feelings and intentions, and his actions based off his feelings and intentions all have a predetermined outcome of which he has no control.