Thanks for your furthewr questions and asking for me
Yes, as long as you are in the UK for less than 91 days (so no more than 90!) then you will not be liable to tax on the employment nut will always be considerd for tax on the rental income (as it arise in the UK and remains a UK source of income) but you will have your personal allwoances to offset agaist the rents
There are no exceptions to that rule (although if you had to stay for longer due to ill health - then HMRC are willing to disreagrd those days and a day is counted as each midnight that is spent in the UK
And this is due to the fact that you still are registered for the counsil tax and bills so are acting as still a resident in the UK ... so yes it would be better for you to come off all bills and as a voter - but is this feasible with any ongoing medical care you might need ....
You can claim all associated costs with the rental income - such as the interest element of any mortgage repayment, buildings insurance, council tax, the bills etc etc but with your employment then you only need to declare this (and any associated expenses IF you spend more than 90 day in the UK)
Flights back to the Uk - only if they are for the sole purpose of attending to a matter to do with the property.
The associated costs would be internet costs (to reflect the % of the bill arising due to this work) and also a % of electricity but I do no imgaine you incur any other costs.
This training is unlikely - but perhaps you could advise more about this as I would have expected the employer to pay for the cost of this training as you are their employee.