It is fairly straightforward really.
You will have to pay tax on the rental profit, presumably in your case at the higher rate, and only 75% of the interest is tax deductible, so a lot of tax. There is a lot of talk about tax aspects of rental income, my favourite one was the deductibility or otherwise of the NPPR. But at the end of the day you are taxable on your rental income less allowable expenses simple!
However if you can rent the property for €1,200 and the mortgage (is that full capital and interest repayment) is €790, you should still have some profit after tax. And in time you will own the property mortgage free.
Your mortgage contract with the bank probably specifies that it is a home loan and if you rent out the property they can charge you a (probably very much) higher rate. Unless you tell them what you are doing how would they know.
However realistically if the bank are being paid every month I cannot see this ever being an issue. At the same time if you tell the bank what you are doing they may feel obliged to act. If the bank is named on any insurance policy they are notified by the insurance company, just watch that the policy is called something obvious like "Landlord Insurance", just buy regular home insurance and notify the insurance company that the property is rented.
I would certainly deal with another bank, for a new home mortgage. That is always the best option IMNSHO.
Using a management company depends on whether you consider it value for money, and depends on how much spare time you have yourself. It is a time and cost trade off.
Just don't think that having a management company will prevent problems. Something bad can happen with a management company too, and it will still be your problem not theirs.