Which SLK file ties the data from AbilityDataSLK to what the spell has to do?

K, heres my q:

You can categorize all spells into several categories (summoning like Feral Spirit or Water Elemental, or Inferno) damaging (Fire Bolt, Shockwave) various negative spells (stun/ slow) and positive (haste/ increase speed/ armor etc) and mixed (Inferno). Say I have a very specific spell (change night to day and make occasional lightnings strike enemies). How do I code this? The AbilityData seems to contain only the basic data about abilities, ie how long they last, how much mana they cost etc.

triggers..........

1) The ability behaviour is defined by the id in the code column in AbilityData.slk. There is a limited number of built-in ability behaviours.
2) Therefore, as Salaam already said, you have to do it by triggers/jass.

Where is the ability behaviour code? Where can I find the script that makes "possess" take control of other units? There are these columns for every level of each skill: Data1B, Data1C etc. What's the point in them?

The code is the second column to you right its 4 letters, like for example AOeq (Ability Orc Earth Quake)

and this code's behaviour is defined in a dll file I think. So you cant edit the codes behaviour

Yes, the ability behaviour code is hardcoded into the WC3 game engine, and therefore not editable.
The DataA1, etc. fields hold some ability specific data. What they actually do, varies from ability code. The Object Editor can help you find out what they do (you have to switch between Raw Data and normal view).