Hi Alex and welcome to the LOC.
As this appears to coincide with the alternator being replaced I would be looking around that area, was it a recon or new OEM replacement?
With all the symptoms it would suggest the voltage regulator within the alternator is playing up, a loose connection or poor earth.
Easy way to check is to check the battery voltage and see if it is varying with the RPM or get one of those cheap cigar lighter socket plug in voltage display units which would be easier to monitor while sat in the car.