If you are unable to provide valid mobile number or credit card then you will be unable to verify your Developer Account.
By valid mobile number, I mean in the terms of Facebook. I have no doubt that you have a valid mobile number!
Taken from this Facebook FAQ Article
How do I verify my developer account?
Facebook has several features in place
to limit the potential for spam and
abuse on the site. Verifying your
Facebook account helps you retain
control of your account and apps on
Facebook. There are two ways to verify
your account. First, you can verify
your cell phone, which allows us to
verify that a real person is in
control of the account. This process
is explained here.
The second way to verify your account
is to add a credit card to your
account. You may do so here.
Unfortunately, if you cannot verify
with a cell phone or add a credit
card, you may be unable to verify your
account. All developers must be
verified before they can create a