There should be no taxes due on the estate at all, since it is less than $2M. Attorney's fees can vary, of course, but it will probably be between 3% and 5%. Other expenses would include paying for any bills he incurred prior to his death, plus funeral expenses, and any expenses associated with administering the estate, such as attorney fees and court costs, and possibly fees to the executor (if he's a paid executor, as opposed to a family member) and expenses incurred by the executor such as travel costs. As for how long it takes - it usually takes between 9 and 18 months - here's a typical time line:
No-Probate.com :: Estimated Probate Time Line
The process tends to be very conservative - the last thing the executor wants to do is make a distribution to the heirs before he is absolutely sure that all creditors and estate taxes are accounted for.