Forgetting all fiction what is the current status of time travel theories? Is it any way close to what we learn in school where time is linear and that's it? Or if so does it have something deeper?

In short, time travel means nothing without space travel. Earth is rotating around the Sun (Sol star), Sol rotates around the galaxy and the galaxy is also moving. So say you want to prevent the assassination of JFK, you’re not just talking about going back 66-67 years, but say you don’t even care where on Earth you end up, where was Earth then? What’s your point of reference? Your point of reference moved.

I think (based on our understanding of the line between the quantum world and thr macro world), time travel is just fantasy.

While mathematically time is reversible for sub-atomic particles (quanta), that breaks down as you gather more particles together.

But it's been a while since I've read deeply on it.

Isn't space travel based on speed?

Time doesn't exist. Clocks exist.

Not just travel, but faster-than-light travel. Either one implies the other.

Time follows geodesics on a curved spacetime manifold, so it’s linear locally but not necessarily globally. In theory a manifold with the right curvature could have geodesics that form loops (which would imply time travel), but there’s no practical way to cause such curvature.