ILR under 10 years long residence

[Sawman]

Hi everyone!
I am in the UK since march 2000 initially on student visa till 2005. switched to residence permit of being parent of EEA child exercising treaty rights. had a refusal of this residence permit in 2007. Reapplied in 2008 and was granted the same visa in 2008. in 2010 applied for ilr on 10 years but was refused because of the gap between the refusal in 2007 and fresh application 2008, and was issued with DL(3+3 years) and will be applying for ILR late 2016.
I have two children aged 11 (irish passport holder,born in belfast) and is applying for BC on form T and aged 10 born in London and applying for BC on form T as well.
My wife is in the uk since 2003 initially as dependent of student and then followed the same path for flr. so she has also a gap in her status between 2007 and 2008.she is currently on derivative residence permit (5 years being mother of irish child exercising treaty rights) with expiry in 2019.
My question is this. Can she apply for ILR on 10 years long residence since she has been legally living since 2007 in her own right in 2017? if yes...what are other requirements apart from residence and english/life in the UK and good character?
Thanks in Advance