Re: Best time of day to pratice?
Usually starting between 1-3 and practicing to about 3-5.
As for mental warmups, part of playing is in your head. I sit there in class and think about playing scales, in two octaves, and possibly ascending in 3rds and 5ths. Even thinking about doing it properly is slowly training your mind, and you'll find that even thinking about running through practicing will make you fingers more nimble because the mental portion is already there, you already know where your fingers should go and at what pace.
That technique is one of the ones I used to finally break the 16th notes at 120 barrier.