I have experience only with the Very Large Telescope run by ESO in Chile, maybe what I write is only valid there.
There is usually no real schedule of targets for ground-based telescopes.
There are two ways chosen at the telescope: either the astronomer who wrote the application is sitting there and decides what to do, or the staff goes through a list of approved programs and looks for objects that can be observed. This depends on the constraints described in the program (usually atmospheric conditions and height of object above horizon). Which target is chosen next is usually decided during the observation of the last target, there is no real schedule.
This is of course different for robotic telescopes (which is absolutely not the standard), like the Hubble Space Telescope but also ground-based robotic telescopes. But I'm not aware of a live feed of the pointing coordinates for them.
What one could do is regularly query the ESO archive[1] as finished observations appear there immediately (I think) and contain coordinates (just enter night: "2020 01 01" and maybe chose type: object).
In case of the Hubble Space Telescope and also ESO's telescopes, you write a proposal containing the science case, the requested time and instruments, and related previous experience, submit it before a deadline (twice each year for ESO) and hope for the best. The acceptance rate for the HST is currently ~20% [2]. It's a bit better for ESO telescopes. If you are successful you do not have to pay anything. ESO even pays your flight and hotel next to the telescopes in the middle of a desert [3].
The situation is totally different for American telescopes (as far as I know), where you either belong to an institution that has telescope time or not.
Also, how can researchers request/rent usage of telescopes (especially satellite-based ones)?