Layout using the numeric keypad (order doesn't matter):
7 8 9
4 5 6
1 2 3

Level - Spell: Combination

Air:
4 - Shock: 9
7 - Enchanted Shock Arrow: 9,8,6,2
14 - Lightning Bolt: 9,4
19 - Invisibility: 9,5,2
22 - Shock Shield: 9,5

Fire:
2 - Fireburst: 7
7 - Enchanted Fire Arrow: 7,8,6,2
13 - Fireball: 9,6,7
16 - Fire Shield: 7,5

Earth:
3 - Poison Cloud: 1
7 - Poison Bolt: 9,1
11 - Enchanted Poison Arrow: 8,6,2,1
13 - Poison Shield: 5,1

Ice:
3 - Ice Shards 1,3
7 - Enchanted Ice Arrow: 8,6,3,2
13 - Frostbolt: 9,3
19 - Frost Shield: 5,3

Spellcraft:
5 - Light: 8,5
5 - Darkness: 5,2

Anyone else got some?

9 is shock

"7,5" Fire + Balance = Fire Shield, +35 Resist Fire.
"9,6,7" Fire + Air + Physics = Fireball, Ranged damage spell.

Don't have the skill to cast "9,5" yet but fairly certain that's just a +35 Shock Resist.
The 3 spells at the bottom of the OP are simply more enchanted arrow versions, one per element.

Thankies for the updates

This might be the wrong topic, but is there a way to hotkey spells? The existing menu seems somewhat cumbersome, having to key it in every time you wanna cast something.

Topic related: What is available at what levels?

I like to discover things on my own, but cant discover this one - Fire spell lvl 7
Tried 7, 5 but (Fire shield) but that's not it.

It's enchanted fire arrow

Ahh I see, I thought it was a higher lvl spell.
Thank you very much.

How do you recast the last used spell without having to select the runes all over again?
Thank you.

Here are the spell I found.

Does anyone know if there are any heal spells? I am starting to think the game was designed for healing to be done through resting, walking around, and herbs/potions.

There are no healing spells. Your best bet in combat is to have healing potions ready.

here is a guide with list of all the spells along with descriptions:

Legend of Grimrock List of all Spells

I find it too cumbersome to have to open your inventory to quaff a potion while mobs are hitting you. I would like hotkeys to automatically drink potions.

yea there should be some hotkey or quick menu for potions