As long as you want really. Say you have 100M shares outstanding. You do stock buy backs over the years now there is only 50M shares outstanding. You do a two way stock split, now there are 100M shares outstanding again.
Yes, though in the US the capital gains tax (for investments held over a year) is quite often lower than the tax on dividends (which are treated as income).
Private persons have to pay income tax when they sell their shares for a profit. So there is no way to avoid the income tax and getmoney out of the company without taxes.
There is no such thing as "capital gains" tax, everything is covered by income tax, at the same rate. You can't use the US tax system to cheat Estonian taxes:)