Conditional Format - Due Dates - 2 questions

I have a spreadsheet that tracks due and past due dates.

The default color of the spreadsheet is black. A is the due date column. B
is the completed date column

The irst furmula in B is =$A1>=$B1 to track items completed before the A1
date, set to blue. Second one is =$A1<$B1 to track items completed aftre the
due date, set to red.

Sometimes there is no due date though. In that case it changes to red and
looks like it was completed late.

1) Is there a conditional formula that will ingnore A1 if it is blank, or
change to black?

2) My formula of =A1<=TODAY() make the items past due red, but it also makes
everthing due today red as well, but they are not actrually overdue until
tomorrow.

Thanks!