All ICANN accredited registrar's are required to provide domain name holders the ability to transfer registrations between registrar's. There is no requirement that they provide an easy to use form to do so and many require that it be done through a help desk ticket so that they have an opportunity to find a way to keep you as a customer but if you are adament on the transfer then they must provide you with the auth code for the transfer which you can give to the new registrar.
There are only a few grounds under which are registrar can refuse a transfer request and those are...
- Evidence of fraud
- Uniform domain-name dispute resolution policy action
- Court order
- Reasonable dispute over the identity of the person authorising the transfer
- Domain name is on hold due to payment owed for a previous registration period
- Express written objection from the domain name holder
- Domain status is in "LOCK" (Registrars must provide a readily accessible and reasonable means to remove the lock status)
- Domain name is within 60 days of initial registration
- Domain name is within 60 days of a previous transfer
Registrars are also required to specify a reason why they are denying a transfer request or refusing to provide the auth code for the transfer request to be initiated by the new registrar.
If they continue to cause difficulties and not provide the auth code then you can speak to the new registrar you want to go to who can raise a dispute with ICANN who will then intervene on your behalf. This sort of dispute can be raised by any ICANN accredited registrar but standard practice is that it is the expected receving registrar.
As for the privacy settings there is no requirement under ICANN for there to be private registration details attached to the domain name and so there is no real resolution except through the original registrar to deal with that aspect. If you are unsatisfied with the registrar's handling of the situation you can request to speak to a senior customer service manager or request that the matter get escalated and they should act to do so but unfortunately there is no guarantee.