On what you said about where to start a lead in E. I think you know, when playing in E. It doesn't always have to start on E, B (subdominant) is also a very common note to start any piece with. But you can start anywhere you want, if that's what you wanna hear. Also when changing chords or keys within a solo, starting with the key note on each chord change will produce more of a boxed in solo effect. Everytime you change a chord, the solo's tonality will also change with the chord. You want to stay away from this. To avoid this, you need to make the solo mix a more melodic flow. A solo is a piece of music in itself, so it should be treated that way.
To help on the subject:
When writing music, I was taught over and over that the focus point should always be written first for that particular scene in the music. Since a guitar solo is the focus point, it should be written first. The reason why, their are alot but I'm just gonna give a few, is because the solo needs to sound good as one piece of music BY ITSELF, that's why it's called a solo. When the listener hears a solo, thats what they focus on, everything else just blends behind it. Because of this, the solo should show the musical progression of your music without limits. The solo shouldn't harmonize the rhythm, because you're limiting yourself before you write the solo by the chords your using in the rhythm. Each time you write a chord before the solo is written, your taking a bite out of the possibilties in the solo. You probably find yourself working on a solo, and thinking "man I wish I could do this, but it doesn't fit the rhythm or the chord progression". Theory also works much better this way. When you look back at the solo you wrote and see that you wrote this measure of the solo in D Mixolydian scale, you know that a A7th chord will work great for the chord behind the solo. Sometimes you'll know just by hearing what you want there. It's easier to think of one note that sounds good, rather than 8, 16, etc. As for those who are concerned over the key of the solo. If the song is in the key of E, base the solo in the key of E. The chords will stay evolving around the key of E also, and it will work out fine. If that's not what your coming up with, don't worry there are these things called Pivot chords. You'll be able to get back to the original key. Just follow your musical instinct.
Most of the seasoned players on here, already have a way thats works great for them. I am not trying to change their ways, or say that they're wrong or say this is the only correct way. Whatever works for you, works! Although I hope I helped anyone, who may have had some of these problems with solos.
"My whole life is a dark room...ONE BIG DARK ROOM" - a.f.i.