Whether you want keys really depends on the kind of tunes you are drawn toward. I barely touched the keys for 25 years, but I’m playing these days with an East Galway style fiddler (lots of Fahy compositions, tunes in Dm, etc.), and in some of our sets I am using 7 of the 8 keys on my flute.
As for tone, I’m not big on exercises in general but this is the one area where I make an exception. I’m pasting below some instructions from an email I just sent to a friend who was also asking for tips on improving tone. Note that people who favor a relaxed embouchure would disagree with some of my explanation below, but I think working toward the goal of achieving quiet, pure, non-breathy harmonics can improve your tone in regular playing no matter how you blow your flute.
I learned this technique from a friend who learned it from Jean-Michel Veillon, the Breton flute player. Jean-Michel refers to it as “the keys to the kingdom,” because it develops your embouchure in such a way that it can make just about everything else (tone, tuning, breath control, etc.) come together on the flute like magic. Basically what you do is play one-handed scales, starting in the second octave, and using harmonics to get the notes above second-octave G.
What’s a one-handed scale? You leave the fingers of your top (left) hand down the entire time, and play the whole scale with just the bottom three holes using your right hand. If you imagine o as an open hole and x as a closed hole, it looks like this:
xxx xxx (second-octave D)
xxx xxo (second-octave E)
xxx xoo (second-octave F#)
xxx ooo (second-octave G)
xxx xxx (second-octave A, achieved by blowing a harmonic --I’ll explain below)
xxx xxo (second-octave B, harmonic)
xxx xoo (second-octave C#, harmonic)
xxx ooo (third-octave D, harmonic)
The harmonics are the keys to the kingdom. You get them by tightening your embouchure and blowing with a very focused stream, not blowing harder but faster/more concentrated. At first these notes will probably sound loud and breathy, but your goal is to get them to sound quiet and pure, with as little air noise as possible. If you work on this every day, or even every other day, or even just a few times a week, just for 10 minutes or so, it can do wonders for your tone.
I think what this amounts to is weight-lifting for your mouth muscles – it strengthens them in a way that allows you to achieve a strong, focused tone in the first two octaves of the flute, and you find that as your tone improves, everything else on the flute sounds better: the flute sounds more in tune with itself and you have more control in general.