Here is what I suggest you should do :
1) Everything you play, try to sing using DO RE MI system or A B C system. If that sounds to complicated HUM each note but make sure you do some sort of sound producing with your voice.
2) Try to play a note then sing back that note; you can also sing then play a note, or try to do it at the same time (sing + play). This is most useful thing out there for ear training.
3) Take scale runs, arpeggios, chord tones, chromatic approaches, pentatonics, solos you love and sing each note before you play it. That will make your voice chords and inner ear stronger which will later translate to your composing and improvising skills.
Regarding fast playing... Yes you can sing fast passages ! I don't use Do re mi nor A B C system when I am thinking of fast passage but rather things like Ti ru ra ri as it is much easier to sing that way when singing fast lines.
You should at all times know the note you are playing but once things get too fast technically speaking then its all a matter of sequences, patterns and licks that you practiced slowly for million times before hand and just speed them up in that given moment. Even then, you still know the notes since you practiced those ideas before
Hope that helps man