Really hope somebody could help me out (Student Visa etc)

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Hi everyone, its the first time that I post on this forum, hoping to get an answer on my situation. As i had no idea who to turn to for an answer on my situation.
I have been studying in the UK for more than 10 years (From College Year 8 to a completion of undergraduate degree and 2 years of master degree).
So basically my situation is that, i have applied for a master degree (2015-2016) and got a visa/BRP with the expiry date of 01/01/2017. As my course suppose to be finished on by the expiry date stated, however, due to medical condition, i wasnt able to complete the master degree, and applied for a leave of absence; Hence to complete my third semester for the completion of my master degree. My university requested me to email them to regain my student visa when im ought to return to study (March 2017).
I went back to my home country during summer 2016, and came back october 2016. When i went pass the immigration, i told him that im here to continue my study (Which i was intended to), and planned to stay in uk and to re-apply for my student visa in March. And thus, he didnt stamp a travel visa considering that my BRP is still valid by that time, and im intended to reapply my visa. (To note: From where i am from, travelling to uk doesnt requires a visa with the purpose of travelling, with a max days of up to 180 days, if travelling, the immigration would usually stamp the date of when you should leave).
So when it gets to March 2017, I didnt reapply for a student visa via university, as i have been unfairly treated by several university professors, and assigned me an impossible mission to complete for my master dessertation. Thus, i havent applied for a new visa.
So my question is that:
1) Am i violating any immigration law of overstaying, if so what are the consequences, and what are my best solution?
2) I had left UK to Iceland during December for a few days, and went back to UK afterwards, does count as re-entry? As i know for the passport that im holding, im allow to stay in UK for travelling purposes for up to 180 days, would that re-new my allowance on the length of stay in the UK?

Thank you very much, god bless you all!

[CR001]

1) Am i violating any immigration law of overstaying, if so what are the consequences, and what are my best solution?

If your visa expired on 1/1/2017, you are an overstayer and have no legal status in the UK and you can be deported.

2) I had left UK to Iceland during December for a few days, and went back to UK afterwards, does count as re-entry? As i know for the passport that im holding, im allow to stay in UK for travelling purposes for up to 180 days, would that re-new my allowance on the length of stay in the UK?

Absence does not get calculated on calendar years. It also depends on what basis you are asking the 180 days limit question. You cannot use your period of overstayer since your visa expired as 'absence'.