Your first step in regards to seeing the kids is to set up a family dispute resolution conference. Legal Aid can do this for you, and both parties are usually supported by a solicitor. Be prepared for a waiting period - ours took about four months, and would've been maybe three if there wasn't a minor run-around with Legal Aid.
In FDR, the aim is to help the parents reach an outcome that reflects the best interests of the child, which (provided there are no significant risks of violence or harm to the child) means having a meaningful relationship with both parents. Both parties are expected to make a genuine effort to reach an outcome, which means discussing and deciding on the 'time spent with' and 'communication with' each parent, among other things.
No matter the outcome of FDR, a certificate will then be issued, which is needed before you can begin the court process. This will also be given to you - and as I understand it, only you - if the mother refuses to attend FDR, or refuses to negotiate 'time spent with' provisions. That means she will be unable to pursue court if the mediator deems her to be unreasonable in negotiations, but you will.
In terms of child support, it is important that you continue paying according to the assessment. My non-legal opinion is that a parent who refuses to support the child emotionally by giving access to the non-residential parent, should also be refused financial support by the non-residential parent, but that's irrelevant until the system is fixed. Anyway, the court does consider how supportive you have been to the child, so while you may have been unable to contact or see the children, you will be able to show you are still committed to their upbringing financially.
So, I guess in short...
Will you get phone calls and visits if it goes to court? Yes, provided there is no risk of family/domestic violence, or exposure thereto.
FDR first, though. Keep paying child support. Be civil to the mother no matter how angry she makes you. Remember, being the reasonable parent always looks better than being the troublesome parent. And contact Legal Aid for free legal advice and to organise FDR.