Mainly you can write off more expenses and you can distribute only necessary profits (i.e., if you have $100k, you can send $40k to yourself and pay only personal income on the $40k).
Don't it depends on where you live. Usually in Europe at least you will be taxed from any income in this company unless you can show substance which gets more difficult to do every day.
Depends on the state the company is incorporated. Yes you can hold them in a brokerage account, but you need to have them invested, not just USD sitting there. So you need to have unrealized gains sitting in your brokerage account