I will try and assist you further although I had opted out previously. In response to your further queries:
can you kindly tell me what difference will it make to her to have a residency permit ?
She will be in a stronger position to sponsor you for residency under EEA regulations and once she has Permanent Resindency( PR), she does not need to be exercising treaty rights in the UK.
will that change any of our circumstances or our right to marry while she is on state benefit ?
If she is on state benefit, she is not deemed to be exercising treaty rights and therefore not eligible to sponsor you.
how long does she need to be working inorder for me to qualify to launch an application and how much income does she needs to be on ?
No rminimum requirements for income etc, as long as she is working i.e. exercising treaty rights, you may lodge your application. Remember she is only entitled to reside in the UK longer than 3 months if she is exercising treaty rights i.e. working, studying or being self sufficient (paying for her upkeep without help from the state). Once she gets PR, she is free to do whatever she wants and can claim state benefits and still sponsor you.
do i need to close my asylum status or is the marriage dealt in different immigration department other than my asylum office ?
You will be asked to close your asylum case if you lodge an EEA2 application for a Residence Card as you cannot have 2 or more applications pending at the same time.
what about missing to sign at the police station will that be a risk to be arrested from the register office ?i dont have passport to show the register office will they accept my asylum id or do i need to apply for new passport.
You need to check with the Registry what they will accept as they may be flexible. As you are not reporting to the Police Station, there is a risk that the Registry may tip off the authorities about your proposed marriage and you may be arrested and detained at the Registry.
As you can see, your case is complicated and you should appoint an immigration solicitor to assist you with your applications to the Home Office, this is a Question and Answer site.
All the best and please leave feedback