I think your alternator may need attention. IIRC they are around 80 amperes max output. This type of power should handle any load [ie lights, fans etc] that is demanded of it. The electrical equation here is Power [in watts] = Volts [12.8v or so *times** current [in amperes] As an example, 2,.. 50watt headlamps = total power of 100watts. Now re-arranging the formulae to make Current the subject Amps = Power divided by volts. Or to apply values,. amps = 100 divided by 12 = 8.33 amps. So it can be seen that with headlights on, the alternator only has to supply 8 odd extra amps,..plenty of current left [80A minus 8 = 72 amps left. If the alternator is running at less than full available power [due to worn brushes or power-diode probs or a fractured solder-joint in the windings] its available power may be well down,..giving the symptoms you have mentioned.
One rough test is to sit in the car while its idling. While watching the tacho, you switch on your headlamps. Now if the alt is working well,..it will immediately start supplying more current out which means the engine will get a higher load as the alt becomes more difficult to spin. This will show as a slight drop in engine revs. If the engine doesnt drop revs slightly, the alt needs attention... You have mentioned the dimming of your car's headlights and the fan slowing down. You're right,..it's not normal and maybe the alt or loose and dirty connections on the alt, or the wiring to the battery. Unless you can get a hold of a multimeter to check the alternator's output volts [nominally around 12.5 to 14v] you'll need to get it checked out.
As far as the battery goes, as long as it is showing full charge thru the spy-glass, and it spins the starter briskly,..its OK. However you need to remember the battery charge is only as good as the alt performance.
JJ