You have to draw the absorption curve between the wavelength and absorbance, by changing the wavelength and measure the absorbance for the same sample.
It is possible only if you have diod array spectophotometer where white light crosses sample, then it is dispersed and for each vavelength is separate diod detector. In case of scanning spectrophotometers, where light is dispersed in front of sample and there is one detector for each wavelenghts it is impossible.
I do not understand the question. With a single beam you should measure a blank sample with your solvent, then measure your unknown compound in the same solvent and there is your spectrum.
that's not correct. For example the Varian Cary 50 is a single-beam spectrometers with a photodiode detector and does measure very accurate absorbance spectra. The trick is to reference the light intensity in the light beam before it hits the sample container. This principle is also used in all absorbance microplate readers...