PhD student applying ILR with extended research outside UK

[Henry_dos]

I am a EEA citizen who arrived in the UK in october 2009. In a few months (october 2014) it will make 5 years that I will have been in the UK, and I am thinking to apply for ILR (or PR?), then wait the required one more year to apply for citizenship, if my understanding is correct. my situation is the following:

october 2009-april 2010: residency proven with bank statements
april 2010- sept 2012: residency proven with bank statement + payslips + P60's
oct 2012- now : PhD student with scholarship of £1000/month.

However, my University has sent me into extensive period of research in the US ( 4 months in the US in 2013, and it will be another 4 months in 2014). I am still resident in the UK, since I have been sent by the University, and I am full-time PhD student here in a very good "red-brick" University, but my passport will show up my entry and exit dates: can I still apply for ILR, and later citizenship, or will these stay count against me in my application? How can I make HO understand that I didn't "leave" the UK during these extended period? Does this problem makes it pointless to apply?

[Jambo]

Your residence should be fine. See Q1 in EEA FAQs - Common Questions - Read before posting - Permanent Residence.

You should be more worried about health insurance (CSI or non UK EHIC) for period of study without employment.

[Henry_dos]

Your residence should be fine. See Q1 in EEA FAQs - Common Questions - Read before posting - Permanent Residence.

You should be more worried about health insurance (CSI or non UK EHIC) for period of study without employment.

If I get a CSI, it will not have covered my past time as student, since it would start now: would it still be ok? I am confused because sometimes I read that we need a CSI "at the time of application" while in some other posts i read "covering most of the time as student". I aim to thus get a CSI after I get back from US, three months before i submit a PR application: would it be ok?

PS: I do have NI number and NHS number as well...