ToME: the Tales of Maj'Eyal

If a weapon has damage (melee) 10 lightning and also has changes damage 10% lightning does the boost in lightning apply to the extra melee? Also is there anything that universaly shares a cooldown? Just got this game 9 days ago and ive died too many times from not paying attention to the skill description, rush being one of them. im curious if i should be saving gear for specific instants like resistances and x type of damage because ive been using the box alot ive only gotten as far as the sandworm tunnel and died to impatience.

+% damage applies to nearly everything - so in your case, the lightning proc would deal 11 damage.
Generally most things don't share cooldowns unless explicitly stated - charms are one example (many items with usable effects will have a description saying 'uses this places all other charms on cooldown for X turns', marking them as a charm).
Generally specific damage types on gear isn't a big deal, some things are vulnerable/immune but it's rare unless you're playing something that only deals 1 type of damage (e.g. a Corruptor vs a Worm that Walks and it's 100% immunities generally isn't much fun).

Thank you

You might want to look up the list of Tier 1 dungeons, and do all of those first for the items, artifacts and xp.