I'm hoping someone could shed some light on some questions I have regarding application for permanent residence, with the subsequent aim of applying for British citizenship. I hold an EU passport (Italian), and I've been living in the UK consistently since 2010. But there are a couple of things which are still not entirely clear to me (apologies in advance for the long-form

1. (lack of) Comprehensive Sickness Insurance: I went to Uni from 2011 to 2014. So, technically, I didn't spend the required 5 consecutive years to be eligible for residence.

However, I’ve been in both regular, part-time employment, and registered as self employed whilst studying, so I was not just a student.
Will that be accepted? And what evidence will suffice? I have self assessment documents from 2011 till present (downloaded from the HMRC website). I was also in part-time employment, at a single workplace, from 2010 to 2013, but I only have a P45 from that job which states the date in which I left. I can however obtain a statement from that company's accountant to confirm the dates in which I was employed by it. Will that be enough?
2. Name change: I changed my name by deed poll in 2013 (not through marriage, I just never liked my old surname). I use my new name on all of my legal documents - bank statements, bills, driving licence, etc, but my passport hasn't been changed yet.
I’m only just in the process of changing it on my passport as it was unaffordable to me at the time, but the name change through the Italian embassy is a notoriously long process (it can take up to two years, and that’s just for the details to be registered, before even being issued with a new passport).
With that in mind, what name should I apply under? Will they accept an application with my new name if I provide a name change (deed poll) certificate? As literally all of my other documents are under my new name.
3. My unmarried partner (who is British) and I have jointly received working tax credits for a few years - will that in any way work against me? i.e. do they penalise you for getting financial support as an EU citizen? Common sense tells me that it's not the case, but the whole CSI deal has completely changed my opinion on what is sensical and what isn't.
Thank you for you insight, it's much appreciated.
AJ