I would appreciate any advice very much. I am a Latvian national with a 2 year old daughter. I am currently unemployed, receiving Child Benefit and Child Tax Credits. Doing a law degree through Open Uni distance learning. I am on the second out of four years of studies. I get financial support from the uni, that covers my tuition fees and also get a grant payment of £265.00 per year (part-time studies).
My husband (Fam. Member of an EEA Nat.) had left us in November '11. He has been working in construction for 4 years as self-employed, had very good earnings until the crisis. After, he had been on and off work all the time, so claimed tax credits in 2010. His current job barely covers his own living, consequently he cannot support us. I am now responsible for paying rent for our house, bills, etc. I wanted to see what financial support I am eligible for (apart from what I already claim), as obviously it is not enough to support my child and myself.
I had made an application for HB, CTB and Inc.Support as soon as he left, but they refused me (habitual residence test failed). I understand "to legally reside" I must be working (which I am not) or be a self-sufficient student. If I start part-time work now and apply again, will I succeed? Will they consider it as a genuine and effective work? Is there any other benefit that I am entitled to claim instead?
I guess I do not qualify for PR too. I came to live to the UK in Feb 2007 (5 years ago in 9 days), but I was working illegally (as found out later), received cash in hand and I have no proof of that employment. I changed my job in the summer '07, applied for NI and paid income tax. I had been in employment until Sep '08.
Then, we got married in Nov and when we planned to submit the application for my husband's visa, I had learnt that I needed to register for WRS. (Not a single employer had asked my registration or told me that it was required.) Therefore, I do not know whether that period qualifies for PM. Have I been working legally if I paid NI contributions, income tax, but had no WRS for A8 country. Does the abolition of the scheme this year has impact on that?
New job in Dec '08 and registered immediately, got the certificate, my husband was issued a visa for a year. I had completed 12 months, fell pregnant, he was issued the Residence Card for 5 years. I was given a residence reg. cert. too. I went on maternity leave; after it I ended my employment (Aug '10). I could not leave my baby and wanted to raise her until she is 2-3 years myself. I still think she was too young to go to the nursery and be apart from me

In Feb '11, I had started my degree, and until researching the law today, had no idea that I need to have a comprehensive medical insurance. Again, have I been residing illegally (for the purpose of PR)?
I really do not wish to quit my studies and leave the UK. I am a very good student and I plan to become a lawyer. The course I am doing concerns laws of England and Wales, so practically I will work here upon completion. I am taking up several modules at the same time to graduate faster and start working (therefore, it takes me 4 instead of 6 years). It would be impossible for me to get a full-time employment, study and being a single parent. Also, the childcare is so expensive!
I am settled, have my family and friends here. Is there really no temporarily support available for me and my daughter until I graduate. I am willing to stay in this country and pay taxes

P.S. Sorry for so much info, I just thought all these facts might be relevant...