I am playing a solo mage character and as a result I am carrying around TONS of mana and healing potions. As you can imagine, this does not leave much space in my inventory.

In the same way as the keyring -- is there an item I can purchase to store these items in rather than them taking one inventory square EACH?

No such item exists, unfortunately - though as you probably can see, stackable potions would make an already serious mage balance problem that Arcanum has even worse.

If you can get enough money, it's a good idea to stock up on Morgana's Tears, since it restores Health and Fatigue, up to 120 points each.

(The indirect solution, of course, is to limit mana drain, that is - max out the Heal Rate and get a Mana +80 Arcane Staff. But you've probably done this already.)

No, but you can store them in a container like a chest or a trunk and they won't disappear. For magick users the best one is probably inside the inn at Blackroot. If you manage to get the Teleport spell, you always appear right outside that inn, so it's very convenient. Just don't put them in a waste basket.

But no, there's no backpack or large sack or anything like that.

Another tip: the only time you need to choose between quaffing a potion and actually spending real time resting is inside of a dungeon. If you're outside or in town, you can sleep for one hour to recover all fatigue, at the cost of having to recast any persistent spells. But taking the option should save you numerous potions in the long run.

Also, late in the game there will be the opportunity to master one spell college of your choice, which halves the casting cost (though NOT the maintenance cost) of all spells within that college. The only prerequisite is that you must have learned all five spells in that college, and then pass a little test.