What is the foundational book of Czerny finger exercises for piano?

Czerny's most famous books of exercises, School of Velocity, Op. 299 and The Art of Finger Dexterity, Op. 740, are great examples of studies that one should be able to comfortably play before progressing to the next stage.

1. Which is better Hanon or Czerny?
2. How can I improve my finger strength for piano?
3. Are Hanon exercises useful?

Which is better Hanon or Czerny?

Czerny is more 'musical' than Hanon, so maybe more enjoyable. Hanon is much simpler, and much easier. The thing about scales is that they are good, but they are one type of pattern only: the etudes/exercises are much more varied (and Hanon includes scales and arpeggios). Schmidt is also good.

How can I improve my finger strength for piano?

Playing exercises from technique books, stretching the fingers, using a quality piano and consistent practice are all major factors of building finger strength. Rest also plays a major part in not overworking the muscles in the fingers so that you can play efficiently.

Are Hanon exercises useful?

Hanon exercises are great for helping you isolate particular "riffs", if you will, that are difficult to play. The idea being, if you repeat them ad naueseum, you'll be able to play them. In the end, any given Hanon exercise will be useless unless you're playing music with figures that are similar to the exercise.