Maverick Thopterist

If an artifact you control has a mana ability with tap in the cost, activating that ability while casting a spell with improvise will result in the artifact being tapped when you pay the spell's costs. You won't be able to tap it again for improvise. Similarly, if you sacrifice an artifact to activate a mana ability while casting a spell with improvise, that artifact won't be on the battlefield when you pay the spell's costs, so you won't be able to tap it for improvise.

Tapping an artifact won't cause its abilities to stop applying unless those abilities say so.

Improvise can't be used to pay for anything other than the cost of casting the spell. For example, it can't be used during the resolution of an ability that says "Counter target spell unless its controller pays 3 generic mana ."