I'm a contractor now and have been for 13 years. I know how the tax code works
"if you are an "S" Corp. you can draw a salary (what ever salary you want to pay yourself) "
Not true. You must pay at least market wages. Profits over that are (usually) paid as dividends
define "Market Wages". you can't put an LLC or an S Corp in a box. Many, if not most are in many markets and offer many services and products.
And, yes you can deduct mileage. "Home office" to client work is mileage that can be deducted