Imaginary around

Yes.

Pretty sure quick performance gives not only bonus to dmg and star gen but also NP gain as well. 3 for the price of 1.

It gives a bonus to star gen, but not exactly 25% because it increases only card effectiveness and not star drop rate as a whole.

Formula: http://blogs.nrvnqsr.com/entry.php/3307-How-many-crit-stars-do-I-get-in-combat

Since it's applied to the cardstarvalue of quick cards it gives you
1st card: 80% x 125% = 100% (20% more crit stars)
2nd card: 130% x 125% = 162,5% (32,5% more crit stars)
3rd card: 180% x 125% = 225% (45% more crit stars)

This value is added to the servant's base star rate, so the effect can still differ from the calculation above. If I calculated correctly, Jack will have a star drop chance per hit of 205,5% of her third card without imaginary around, which after 5 hits translates into around 10 crit stars. This is assuming all other modifiers can be neglected (not critical hits or overkill).
With imaginary around this rate per hit is raised to 250,5%, so around 12-13 stars. This is actually pretty close to a 25% increase of stars.