Is it expected to deliver astronauts to the ISS Crew-Dragon-style, but without the 2nd stage; that is, "FSTO"? (as opposed to SSTO)
Starship cannot get to orbit in any meaningful way without Super Heavy. Theoretically, it would be possible to get to LEO without any payload and by removing all recovery hardware, the body flaps, the landing legs, the heat shield, the header tanks, and the extra fuel for landing. However, doing so wouldn't make any sense.
You need Super Heavy to do anything meaningful … such as bringing crew to the ISS.
If no, can the Super Heavy be made into an SSTO spaceship, capable of ISS docking and vertical landing?
Super Heavy is the booster. It can't get to orbit. And if by some miracle a Super Heavy magically gets transported into orbit, then it can't get back: it has no heat shield, no way to shed its velocity, no way to survive reentry from orbital velocity.
It doesn't really make sense to compare Starship to capsule-based systems such as Dragon, Soyuz, Starliner, Orion, or Apollo. You should compare it to the Space Shuttle.
Starship works very much like the Space Shuttle in that it "merges" the traditionally separate second stage and crew vehicle into a single vehicle. There are only two stages: Super Heavy, which is the booster, and Starship, which is both the second stage and the "capsule". Unlike the Space Shuttle, it will not throw away its tanks.
Starship docked to the ISS will look pretty ridiculous, though:[Source: SpaceX]
Starship's pressurized volume is comparable in size to the pressurized volume of the entire ISS – this means that a single Starship launch will bring as much habitable space into orbit as 12.5 years of construction on the ISS!
However, note that despite the renders on the SpaceX website, there are currently no plans to actually use Starship to launch to the ISS. Also, it is going to be a long time until Starship gets crew-rated as well as certified for ISS proximity operations.
In fact, it is questionable whether that even makes sense: why go through all the hassle of docking to the ISS, unloading all the crew and cargo and the experiments, install all the experiments on the ISS, then after 6 months un-install all the experiments, load everything back into Starship, etc. when Starship is so big and so cheap that you can just use it as the space station?