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Level 7 comes at 19600 exp (Vanilla DS2). Say character has 20000; if this is x4 then without the mod the character would have 5000 exp and would be at level 4; so you have a level 7 mage 1-shotting level 4 monsters.

If only nature magic was used then nature magic skill would be the same as character level. This determines what spells you can use, but their effectiveness depends on Intelligence.

nature_magic_intelligence_influence = 3.0

Intelligence starts at 11 (for a human; 13 for an elf, etc). If the 3.0 applies to levels then level 7 nature mage has gained 21 Intelligence making 32 (etc) whereas level 4 mage has gained 12 Intelligence for 23. If the 3.0 applies to exp then 5000x3 gives +6 levels so Intelligence 17 (etc) without the mod, 20000x3 looked up in the table gives +11 levels so Intelligence 22 (etc) with the mod.

Am I anywhere near right on this?

Skill points. Without the mod character starts with 2 (pre-assigned according to race) and at level 4 has gained another 4, whereas with the mod level 7 character has added 28! Is that real? Have you put all that into Aquatic Affinity and Arctic Mastery? Maybe that explains why everyone is going down before you.