Thanks for your questions
1) Unless you need to complete self assessment tax returns then you will not need a UTR, but just will have tax records under the Employers reference number and within that reference number, your National Insurance number. And if this employment income is your only income and you have no income abroad, then you need take no further action regarding this matter.
2) Initially the fact you had been allocated Month 1 (810L) tax code, does mean a tax refund would be reviewed for, however as you have not spent more than 183 days in the UK you will not be due a tax refund, and as you did not plan to stay more than 2 full tax years, are going to be treated as not resident/not ordinarily resident, so are not due full personal allowances for the year, so the tax you have paid is correct.
3) No as again you will not have spent more than 183 days in the UK, so are not due personal allowances for the whole year, so the tax you will have paid at July 2013, will be correct. You should complete the P85 for HMRC on leaving, so they are aware that you have departed the UK.
I am sorry the news is not better, but you have to be treated as resident from the date of arrival, and your sty here is such a short one, that you are not eligible for the full allowances, only those for the time you are actually in the UK.
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