Typically, VC's will leave the board once they have their exit. Some do stay but usually, a publicly traded company will recruit board members with different talents for the next evolution of operations (i.e. growth).
Stock price does not really affect the cash/revenue of a company. Rather, cash/revenue affects the stock price, among other things. Stock price is really a bet on the future growth of the company, what analysts think the industry will do and if investors believe in the CEO's vision.
After an IPO, the ownership retained by the company depends a lot on what is offered via the IPO. It could be 20% or 80%. It really varies depending on the company.
Jeff's comment is a good one. Due to the SEC and Sarbanes-Oxley, a public company has a lot of restrictions, auditing and liability issues that it must look out for. Since investors want returns, CEO's tend to focus on the next two quarters out and push for profit and growth in the near term. This makes any sort of long term plans difficult to implement but not impossible.