I'm not sure if you can easily disable tooltips during combat. If there is an option to turn them off then you might be able to do it using some UI scripting and the in-combat icon of the player window, but I don't remember seeing an option like that.
As for hotbar cooldowns, they should show up in real-time, so I'm not sure what you mean they didn't. There may be some that show minutes and hours, but that may be a space constraint more than an inability.
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