Landlords insurance - Buildings vs Contents

Good afternoon.
Could someone help me understand this.
I’m about to rent out my furnished flat in a residential building. Obviously, there is an insurance for the whole block via the management company but this, as I understand, has nothing to do with each individual flat? If my boiler or ventilation system break down or water pipe within the flat bursts, they are my responsibility, right? So, I do need to take out my own buildings insurance? Plus contents insurance for the sofas / tables / beds / kitchen appliances etc? Because pipes and boilers are not the same as furniture. Are my assumptions correct?

And if I insure the contents for let’s say £10K, how will I get paid for damages to just a table - the cost of the similar new table, the cost of depreciated old table or £10K divided by the number of the items in the flat (let’s say 100) and 1/100 will be paid for the table?
Thank you for any piece of advice.