1- I am in US and we use Coinbase to buy Bitcoin from bank. Then we transfer that BTC/LTC to Bittrex/Binance/Cryptopia/Kucoin exchanges for trading. What stops these exchanges to accept fiat directly from bank, instead of keeping Coinbase in between ? If somebody come up with that exchange, wouldn't that exchange be more preferrable than others ?
Of course... until the various three letter government agencies like the IRS, FBI, NSA etc all come calling with various rules, regulations, fees, demands... Look at the situation with Poloniex and Coinbase and other US-Based exchanges...
The IRS is coming for your crypto! 
2- If one has to open an exchange in multiple countries, does it need to get approved and some fees associated or any other info ? I understand that there is some regulations, for example, I am in Washington and while registering on few exchanges, if I select WA state, it says you are not allowed due to state restriction. Where that approval is placed ?
All over the place... local government (ie. city/state level)... or government at a federal/country level... Some states (New York is a good example) have implemented various "cryptocurrency" laws... several countries have either implemented various laws or are making loud noises about doing so (ie. South Korea, Russia etc).
Some are looking at "banning" it outright... others are floating the idea of "regulation" (ie. tax, fees, red-tape, forms, ID etc) all in the name of Anti-Money Laundering and Anti-terrorism (and tax!) etc...
