You just cast them like any other mage, select them from her spell menu.
Be aware that mages can't cast spells while wearing anything more than the lighter pieces of armour. Normally a pure class mage can't actually equip such things, but the rule applies to dual- and multi-class characters too. Imoen is a Mage/Thief, so she can wear armour like chainmail, but doing so will disable her spellcasting abilities. Better to stick with things like Shadow Armour (+4 Leather Armour) or special Mage-friendly armour like Bladesinger Chain.
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To memorize spells in baldur's gate - I assume you are talking about the PC game - open up your spellbook. On one side, you can now see the spells you have available in your spellbook. On the other side the spells you already have memorized and those you are going to memorize are displayed. With a left-click on the spells in your spellbook you can select those spells you like to memorize. A right-click on those you already have will remove them. After adding the spells you want, you can see them, but not use them at once. They will be available for you to use after taking a rest. So either do a normal rest in the wilds or pay for a night in an inn. In Baldur's Gate II, there are two more options available: Cast the lvl 9 spell 'wish' and select the option that your party has just rested (which is not always available). This last option is the only available resting option you can use during a fight but since you can completely reload all your available spells and daily abilities during a fight, this is the most powerful one. Nonetheless there is a way to restore your spells without resting: spell trap. This powerful spell (which is also a daily ability of the 'staff of the magi') protects you from spells up to an accumulated level and at the same time restores your own spells, so that you can cast the restored spells again without resting.
I don't know how to get fire spells, water spells, lightning spells etc. but i DO know how to get the Healing spell.
I know how. First, click on the LIGHTING BUTTON, then, click on that spellz you want to use, next, drag that spellz to someone or you then it will work.
No, as it wouldn't have much use whatsoever. Mages/wizards alike use items to enhance spells, not their staves.
The ice spells in the Ancient Magics book. It's members only and you can only use it after the Desert Treasure quest. Ice Burst, Ice Blitz, Ice Barrage, are three of the four ice spells.