2) If you run a bitcoin business, do your records still list all your assets, sales, liabilities, etc. in dollars, or in bitcoin?
Of the businesses listed on GLBSE that actually report financials, nearly all report in terms of BTCs.
So it probably will depend on what currency the business' debt or dividends will be paid in. If the business owes BTCs, that is who will be reading the financials and thus they'll want BTCs. If the business has BTCs investment and pays dividends in BTCs, then those investors will be the ones reading the financials and thus they'll want to see BTCs for earnings and dividends.
Now for tax purposes, most likely every revenue and expense denominated in BTCs will need to be recorded in in its fiat equivalent at the time.
So there will be two sets of books, one used for reporting taxes and one for a different audience.