Hi :)
Its true, any coloured quartz should not be left in sunlight for too long as they fade. If your amethyst crystals or any other crystal is in the form of a cluster, I personally feel they don't need charging as often, as the vibrations seem to reverberate between the many crystals to charge and cleanse one another. If they are in single crystal points, you could charge them on a cluster, with moonlight (full moonlight is even better), or even a thunderstorm. For me though, I dont like putting any crystal at all under the sun, especially noon to evening sun because I feel the energy they suck up is very heavy and "heaty", much like how we feel in a warm room after a heavy lunch :P
Cleansing, you could again use moonlight, thunderstorms and crystal clusters, sound, smoke, running water, burying in the ground, and salt. Caution though, many crystals do not do well in either water or salt, and be especially careful with salt water. Amethysts should be fine, but not amethyst clusters as the underside material may absorb salt water and crack.
I don't do very heavy work with mine so I just charge my smaller pieces on my amethyst cluster and opportunistically charge them in the full moon/thunderstorm, so I can't really say how great the other methods are. Honestly I work them so lightly, I think my crystals could last a lot longer before really needing any sort of charge/cleanse, so I don't feel much difference after the moon/storm charge anyway. Or maybe those methods just aren't very effective haha
Also I'm not sure about putting crystals in freezers or running under cold water. I'd advise that you gradually lower the temperature rather than dumping them straight in the freezer to prevent cracking. Normal physics