True it is not easy to get a bank account in Dubai but not impossible. Make sure you have all your documents ready (and have original copies) along with 3-6 months bank statements.
There are some banks that allow you to submit the application online, you can always try your luck.
You can check out Seba Bank (a swiss bank). Issue is that they require a minimum deposit (300k USD), and yearly maintenance cost is relatively high. Not sure if you find this suitable, but if you find another possible bank, please share.
yes they can, most of the services in Dubai can be done electronically and recurring.
a great indicator to look out for are the developers of the individual buildings. I personally try to avoid Damac.