1) Do I have to pay taxes on retained corporate earnings? - LLC is not taxable entity - all income is passed through to members and will be taxed on individual tax returns.
2) Do investors who buy units of membership pay taxes on their profits at their personal income tax rates? - yes - that would be dividends and taxable for investors.
3) Assuming the company is very profitable, what corporate entity should I treat the LLC as (or convert it to) to avoid the greatest amount of taxes (LLC, Partnership, S-corp, C-corp? - you may convert to S-corp; If you do not plan distribution and plan to retain the income for business - C-corp would be preferable.
4) I plan to break the company into 5,000,000 units. Is this possible? - yes - but it would be important to structure the business to minimize the tax pressure.
Please ask for clarification if needed.