Can I use Improvise to pay for activated abilities?
No. Improvise only works for casting spells. Activating abilities, while similar is not casting a spell, thus it cannot be paid for with Improvise.

111.1. A spell is a card on the stack. As the first step of being cast (see rule 601, “Casting Spells”), the card becomes a spell and is moved to the top of the stack from the zone it was in, which is usually its owner’s hand. (See rule 405, “Stack.”)
112.1b An ability can be an activated or triggered ability on the stack. This kind of ability is an object.