Hi there. Given the information provided I couldn't comment fully on the situation at hand. In terms of the property that you have purchased, if you are resident in the UK, the only expenses you could claim towards this would be estate agent/solicitor costs and/or improvement costs. Improvement costs would only be eligible if the improvement made wasn't already part of the property e.g. installation of a central heating system.
For your second query I would point you towards the links below which give detailed information regarding working from home or in your case a studio that you are renting.