I think Citibank offers one of the best online banking facilities all over the world.And with Citibank its possible to send money to other countries online and their transfer transaction fees are extremely affordable, and exchange rates are among the very best. And there are no hidden charges unlike other services that send the money. I have been using Citibank and the services offered by them are really good..To know more-

With account it is mostly possible to send money online. You need to register the recipient with bank once to enable that.
Charges will differ from bank to bank.

You can check with FBG - If you have their credit card they have a service to transfer the money using credit card on phone & there are some offers also been attached to it.

Most banks have online transfers. Most charge 50-100 dhs for overseas and half that for local transfers. I’d consider opening hours and location when choosing a bank. Many of the overseas banks only have one branch in Dubai and it can be a nuisance to visit.

Most UAE banks have online banking system.
I have used HSBC and they have a good online bankin envt and have quick online responses to your queries.I am not sure of the transfer rates.But shall let u know as soon as I double chek the details