Is any service available to open fast EMI and bank account?

Why do you only have 2 days?

1) Use Localbitcoins or a bitcoin ATM.
2) Use darks

Mister Tango and Kraken coud work for this purpose for you.

takes less than 1 hour to open.

No you don't need any bank account. If you look at the EMI's around you can see that for instant Kraken is offering crypto exchange to FIAT, you can withdraw the money to another EMI say Mister Tango or ePayments and from there to anyone you want.

That said, you should read through the forum and check the different opinions about EMI's. Most don't want to keep a lot of money in an EMI account so sooner or later you want to take the profits out and send them into a bank account, this could be a local bank account which you open in your own name or some offshore account, it is very difficult to open a offshore bank account.

As @darkster already pointed out. There is no need to open a bank account for what you are looking to do. However, take care when working with EMI's you never want to stash your money there but you want to withdraw it to a real bank account near buy you (not an offshore account) or place them in assets.

Why not an offshore account. Isn't it the benefit of having offshore bank account to be able to safe your money long term

the problem with an offshore account is that the most find it very difficult to get an account opened either because they fail to provide documents needed or because of their business activity as well as the agent fucking it all up.