For example if a certain star subtends an angle of 32 arcminutes at the Earth’s orbit and it's light has a peak wavelength of 500 nm, how can I find the luminosity and mass of that star?
The only star subtending an angle of 32 arcminutes at the Earth is the Sun!
The angular size combined with the orbital separation of the Earth from the Sun gives its radius. The peak wavelength gives an estimate of the effective temperature based on Wien's law. Application of the Stefan-Boltzmann law then gives the luminosity.
The only way to get the mass would be to use a calibrated mass-luminosity relationship assuming that the "star" is on the main-sequence. Given that these are usually scaled from the solar luminosity, this is a bit nonsensical - the Sun is a star of one solar mass. You can of course use the period of the Earth's orbit and the size of that orbit in Kepler's Third Law to estimate what that solar mass is.