Question..how do I track my daily cash register income AND bank deposits in the checkbook without having both post as income on my P&L?

There are a couple of ways to handle this . I will give you one expample:. 

1-Make sure you have set up sales items in your items list.  2-Create a sales receipt for that days sales, ( set up a customer called “Daily Sales”) Choose “daily sales” for the customer, fill in the rest of the information on the sales receipt.  At the bottom you will need to select the “Deposit to” account.  Select undeposited funds.  3-go to banking and make deposits.  Select the sales receipt you just entered.  On the Deposit screen select the bank account you will be depositing funds to. Select the deposit date.  in the body of the deposit field, the first line should have already pulled in the amount from your daily sales receipt.  On the second line, select your Cash in Register account.  Under the amount column put a negative number for the amount you will be keeping in the cash register,  On the 3rd line, select your Cash in Safe account. Under the amount column put a negative number for the amount you will be keeping in the safe for change.  Now your net deposit should equal what you are actually depositing to the bank.

How do I run an unpaid bills report and capture the amounts due from 12/31/2010 to match my balance sheet at the same date?

Are sales discounts debited or credited in a general Journal?

When you make the intial sales, the “Sales” income account is credited and any discounts would be debited to “Sales Discounts and Allowances”

How do you record an accrued expense?

Make a journal entry and debit the expense account and credit the liability account(generally the liability account is setup as a current liability and called accrued expenses)

Reverse the journal entry in the month that the expense is actually paid

Where should capital assets be listed?

Capital assets are set up as “Fixed Asset” accounts on the balance sheet