I've beaten Daggerfall before as a fighter class, now I am trying a custom mage. I configured it much like a normal mage, but with these differences:
SP 3x intelligence instead of 2x

Minor skill long blade instead of short blade

Regeneration in darkness (this doesn't seem to be helping very much)

Some resistances (this doesn't seem to be making any difference, I get hurt by the things I am resistant to just fine)

These advantages put my difficulty dagger pretty close to red, which I figured wouldn't be so bad since monsters scale to your level. But I seem to be getting tough monsters WAY sooner than I should. For instance, I saw my first Ancient Lich at level 2 (I ran).

I'm level 5, but I can't seem to inflict much damage with spells, because the enemies keep getting their saving throws. Weak damaging spells don't hit often enough to kill. My workhorse spell has been something I call "Big Hurt." It is an on-touch spell, magic damage, and does 1 + 19-19 per level damage on hit, and uses half my SP. It seems to work pretty well against bears, sometimes is good against humans, but too many of the monsters just make saving throws against it, making me out of SP and helpless.

Zombies for instance are a problem. I seem to encounter them a lot. "Big Hurt" never seems to work. What works more often is Fortify Speed, which I cast and then flail wildly with my Dwarven Saber, and even then I lose more often than I win.

Just now I found an Ancient Vampire. My reflect spell nullified his shock, but didn't seem to hurt him. Then he clawed me to death.

What should I be doing at this point? I thought spellcasters had it easy in Daggerfall.

In my experiences they have it much easier at higher levels, especially since spells cost less magica and are more effective as you gain levels and raise those skills. However when at lower levels, especially under level 12 everything can and will kill you. The greatest advantage mages have is the item and spell creator through the mages guild. I'm not sure why you ran into an Ancient Lich at level 3, unless is was in one of the non-random dungeons, like Scourge Burrow. Also In my experience Regeneration in darkness (it like restores a single point of health every 3 or 4 minutes) and Resistances don't seem to do much, it's better to relay on enchanted items for protections. You could also always play a Altmer and use the weakness to paralyze trade off gimmick (you keep your immunity) to create a more leveling friendly custom class.

Perhaps this guide could help, it greatly helped me back in the day: http://www.tesguides.com/tes2/