How can I avoid paying self-employment and Social Security taxes on money I earn?
You can’t. You can consider forming an S-corporation, and pay yourself a reasonable wage, which is taxed as regular employment income. With an S-corporation, you can take the rest of your net profits out of the company as dividends, which are free of employment taxes (and the double-dividend taxation that happens to C-corporations). But, be careful! If you are grossly underpaying wages to yourself in order to take more money out of the company as dividends, you might run into trouble with the IRS.
If I pay personal expenses out of my business bank account, should I count the money used as part of my personal income, or can I write these expenses off?
You would include the money in your personal income. You would not be able to claim the amounts as business expenses. Only business related expenses can be deducted from your business income. It is recommended to avoid mixing your business and personal bank accounts to ensure business and personal expenses are paid from the correct bank account. Not mixing the bank accounts also allows for easier record keeping to comply with state laws and for the annual preparation of income tax returns.