Have those astronomers any predictions for Tyche's orbital parameters?

Not enough to convince many professional astronomers of it's existence, including myself. It is said be be about 500 times further out than Neptune, or about a quarter of a light year, though this is speculation. This would suggest an orbital period of a bit less than 2 million years, and proponents of the idea also speculate it to have about 4 times the mass of Jupiter. This would be much too small to suggest it is a brown dwarf, which would need at least 13 times the mass of Jupiter for it to ignite. It is said to be in the Oort Cloud, though investigations of old IRAS data failed to find it, which indicates that if it exists, it is much further out than suggested, maybe more than 10,000 astronomical units. All in all, the great majority of professional astronomers view the idea with a great deal of skepticism.