shouldn't negatively impact sleep, unless you suppress cortisol too much. if you notice any issues, you may can back off the time of the second dose or lower your second dose to .4ml.
Anabaholic is correct, we usually don't want you applying right before bed because the carrier slowly released the product over 6-8 hours (b-AET has a short half life), but it will continue suppressing cortisol making it difficult for you to wake up. Additionally, you'll miss managing that evening cortisol spike.
I always apply with my hands...shouldn't be any problems there, as long as you wash your hands thoroughly (if you have concerns about transfer).
.5ml dries extremely fast for most...in San Diego, I can put my shirt on within about 2-3 minutes. In Phoenix (dry climate), I can almost put it on immediately.