How the blueshift from Andromeda galaxy was measured? Since the measurement of blueshift/redshift has to do with the identification of relative distance of spectral lines how this identification is possible under the influence of such a big number of stars with very different characteristics?
It's true that stars can be very different but the spectral lines are the same in all of them, though the relative intensities of the lines will differ from star to star. So if for example you're measuring the Lyman $\alpha$ line then every star in Andromeda will have this line at the same frequency. This allows you to measure an average position for this line for all of Andromeda and get an average velocity for all the stars in Andromeda.
This is what Slipher did in 1913 (I'm not sure what lines he used) to get the relative velocity of 300km/sec.
Because Andromeda is rotating the relative velocity of individual stars depends on their distance from the centre of Andromeda and which side they're on (relative to us). So the 300 km/sec can only be an average over all stars - the lines would be broadened by the motion with the galaxy. For nearby galaxies we can resolve the rotational motion and measure the galaxy rotation curve.
The measurement of the velocity vector of a nearby, large galaxy is not a simple matter. If you just dropped a spectrograph slit down randomly somewhere in Andromeda then you could get a wide variety of answers, since it rotates with velocities of $\sim +/- 200$ km/s in different parts of its disk.
To estimate the centre of mass redshift one must use different tracers at different positions in the Galaxy. One of the more accurate techniques is using Hydrogen 21cm radiation. An early study is shown in van de Hulst et al. (1957). Fig.5 in that paper shows the change in radial velocity as one moves along the major axis of the galaxy from one side to another. One then models these with some density weighted rotation curve to estimate what the centre of mass velocity is (obviously quite close the the velocity measured in the brightest part of Andromeda). van de Hulst got -296 km/s (towards us) with an uncertainty of less than 10 km/s. A more modern value is $-301 \pm 1$ km/s (van der Marel & Guhathakurta 2008).
This line of sight velocity of the centre of mass of Andromeda is incredibly precise, but this includes the motion of our Sun around our Galactic centre. Correcting for this puts Andromeda on a collision course with the Galaxy with a closing speed of around 100 km/s.