Tax rules are very different country to country. I declare all earnings from my music and studio and put in a tax return with the deductions. However I do record other peoples projects so you could say I am not really a home studio but a semi-commercial studio and I play paying gigs and do live sound at venues. I also have a separate building with the studio and gear storeroom due to living in an apartment, the advantage is that I can claim the expense of the building, interest, insurance, electric, etc etc. The studio also owns all of my live gear as well, amps, guitars, PA system, etc, which I effectively hire from my own studio to use for $0. (accountant talk).
Regarding if you can claim part of the mortgage, be careful, if you claim some of the house mortgage for business use you may be up for capital gain on part of any profit when the house is sold. However you should be able to claim part of the electric and insurance, etc, of the building without a problem.
You need to talk to an accountant about what you can claim and the effects of claiming, and if you actually qualify to claim regarding if it is a hobby or part time business.
I have been paying tax on my music earnings for the last 40 years, sometimes the deductions work out in my favour sometimes they don't, if you can claim and you run at a loss, they can reduce your day job earnings as well which then makes it worth while.
Alan.