the first piece of advice i can give you is that you aren't trying to learn a bunch of licks and play them in a good sequence. every solo you play should be relative to the song in which you play it. for example in the jazz idiom, that is how soloing always work, but even in rock, the better artists work with the specific song.
here is a very simple example:
http://www.youtube.com/watch?v=zRGwjByOF7k . Notice how you can hear the words in your head as the guitar plays? This is not a particularly good video and there is no embellishment but what you are trying to achieve begins with something like this and can go as far as essentially 'free-styling' off the vocal. Imagine speaking with the guitar. Like, hear the words in your head, and play the pitches you hear relative to the words. Thats the first piece of advice- reference the other musical material, whether its the rhythm from the drums or the melody from the vocal or other musical instruments; this will immediately give you ****loads of material to work with in every musical situation.
the best way to learn about the other thing you are talking about in my experience is to practice something called a 'double stop'. basically if you just play a note on any given fret, for example the 5th fret on the G string, and then play the 5th fret on the A string (this will be C on the G string, and A on the A string) it will create a minor double stop. If you can play the scale on the E string, you can always find the double stops on the G string that are the 3rd of that note. It will either be the same fret, or one over (for major).
Then to get stuff to sound in key, you just have to learn to harmonize the scale. There's plenty of ways to learn this. I haven't watched this vid but Dave Weiner usually explains **** pretty well so i'm sure he'll teach you how to harmonize the scale here:
http://www.youtube.com/watch?v=xMRCdi_azS8 .
This is a good place to start if you want to introduce chords into your solo. Remember that if you are playing in A minor, you want to harmonize the C major scale. So your chords would be: C major D minor E minor F major G major A minor B minor (or diminished). All those chords will sound good over a minor groove in A, especially if you are only playing roots and thirds, as i mentioned in the double stop example (although you can obviously play double stops with any notes).
Once you can play double stops like that, it becomes pretty intuitive. What i am learning now a bit more is playing larger chords with more tonal colour (eg outside the scale) as well as different voicings (the way you play the same chord on the instrument).
Good luck!