Are the reported satellite velocities, such as for the ISS at 17,450 mph relative to the surface of the earth, which is turning, or to some fixed point without the rotational velocity. In other words, is the ISS moving at the above velocity relative to a point on the earth's surface?
All velocities are relative. In this case, the orbital velocity is in an Earth-Centered Inertial (ECI) framework, so it's relative to a non-rotating set of axes whose orientation is fixed with respect to the stars, and with it's center at the center of the earth.
The OP's question can be restated as "Are satellite velocities stated in an ECEF (Earth Centered, Earth Fixed) frame, or an ECI (Earth Centered Inertial) frame?"
As indicated by David Hammen's answer to What is the frame of reference for orbital speed?, the choice of frame of reference is somewhat arbitrary. However, partly by convention, orbital velocity for a satellite in orbit around the Earth is defined in an Earth-Centered Inertial (ECI) frame of reference, relative to a non-rotating set of axes whose orientation is nominally fixed with respect to the stars, and with it's origin at the center of the Earth. (For reference, see Frame of reference section of the Wikipedia article about Orbital state vectors)
Note that using an ECI frame for orbital parameters, rather than an ECEF frame, makes figuring out how to transition to another frame of reference much less mathematically complicated, e.g., going to the Moon where an LCI (Lunar Centered Inertial) frame makes more sense. This is most likely why the convention of using the ECI frame for orbital velocities was chosen over the more obvious (to an observer on the ground) ECEF one.