If I call my broker to sell a stock at say 10am in the morning and assuming that he does whatever he has to do to sell it immediately, can I assume that it will be sold more or less immediately (within 15 minutes) at the market price?
On a liquid stock a market order fills the time it hits the exchange. Fraction of seconds. The only delay will be the time taken by your broker to enter the order.
On illiquid stock, this can take time. But there are people waiting for such market orders and make tons of money by putting a favourable ask or bid.