Can sinus infection as the result of bad wisdom tooth removal job/ fracture cause spine infection? is there barrier between spinal fluid and sinus?

Unlikely: General body infections usually cannot invade the cerebral spinal fluid. The sinus is not "connected" in a way to the csf.

No spinal connect: There is no connection between sinus and spinal fluid. Your poor wisdom tooth extraction may cause a sinus infection if it was an upper tooth, but not a spinal infection or spinal fluid leak.

Yes & No: A sinus infection may result, though rarely, from a bad tooth infection/surgery on the upper teeth only. This is because the roots of the upper teeth are in the floor of the maxillary sinus. Infection of this sinus results in pain & pressure of the mid-facial area along with congestion and discolored nasal drainage. However, it's not possible that dental procedures cause spine infection.

Yes: If you develop a sinus infection that become blood borne , the infection may spread to bone. There can also be spread to the intervertebral disc . Although the occurrence is rare, it is possible are is recorded.