Thanks for your response ands for taking out the time to post the question again - I'm not sure what has happened, but that actual question has not arrived on the question list nor is showing on your profile of questions,
Anyway - lets deal with your question. Second homes are eligible for a consideration of discount, usually up to a maximum of 50%. but these discounts are at the discretion of the local council.
The laws allowing these were tightened up with effect from 01/04/2013 but when in job related accommodation (which this would not fall within the scope of- as its when property is tied to the job, such as a gamekeeper and a cottage on an estate, or a vicar and the parish house.
The only other time a discount is considered is when one of the properties is vacant - although this discount in the main has been discontinued.
You also ask after single persons discount - do you not get this on your main home ? Or do you have family living there? But single persons discount does not apply to second homes only the main home.