Applying to flr(fp)---need help!

Hi,
I am an urgent situation at the moment.
I was doing PhD course and finished final viva in a college.
I asked them whether I could extend my visa and they said that I could under the Tier 4 Doctorate Extension Scheme for one year.
I applied to visas before my visa expired. But I got a refusal letter from HO and on the basis of the immigration rule
(Paragraph 245ZX (n) (iii) states that: "the applicant must be sponsored by a Recognised Body or a body in receipt of public
funding as a higher education institution from the Department of Employment and Learning in Northern Ireland, the Higher
Education Funding Council for England, the Higher Education Funding Council for Wales or the Scottish Funding Council and that
sponsor will be the sponsor awarding the PhD;") HO says that my college is not entitled to issue CAS for Tier 4 DES.
I and all my family (wife and two children) suddenly became overstayers.

I have been in the UK for 9 years and 2 months with student visas, and my wife and children have been here 8 years 2 months with dependent visas.
So some friends of mine told me that I could apply for flr(fp) private life in 10-year route since my children have lived here more than 7 years.

Is this elegible for me to for for flr(fp) private life in 10-year route and what is the possibility to get the visas as I have heard that this visas are rarely granted.

I have only 10 days to re apply for this visas since the refusal letter was decided on 14 April 2015.
As I don't have money for a solisitor, I have to prepare this by my self.

I need advise from all of you friends.
Thank you.

Please give me some advice!!!

Is flr(fp) is avaialbe for those children who have lived in the UK more than 7 years and their parents?
Can I apply for the visa under 10-year route private life?

I believe you and your wife will have to use FLR(O) as you do not qualify under FLR(FP)'s category.

For the child who has been here for 7 years, you will use the Private Life 10 years route for him/her.

Obie wrote:I believe you and your wife will have to use FLR(O) as you do not qualify under FLR(FP)'s category.

For the child who has been here for 7 years, you will use the Private Life 10 years route for him/her.

Do you mean I have to use two different forms?
could you explain more about the difference betwen flr (fp) and flr (o)?
what about the possibility of having isa under this ategry?