I've stayed at this lovely apartment in the coldest month - in January. The decoration and equipment are perfect for a long-term stay. Location is great - the old city is close, public transport is available around to any part of Riga.
Very good internet connection. I work online, had video calls, all was perfect.
I paid separately for gas, water, electricity, and wifi at the end of my stay. The host kindly make it clear before I booked an apartment and gave all sources to see prices, so I can count my budget before.
The only problem was that a bedroom is located on the corner of the building, no neighbors flats around to keep the warmth. And the building is old by itself. So the bedroom stayed pretty cold despite the heating - cold wind outside basically never stopped. I was able to warm the living room up to +17-18 Celsius (that's enough for me), the bedroom was colder, so I didn't spend much time there except sleeping. With all these conditions my expenses for 28 days in January were 92.57 euros for gas, 21 euros for wifi, and around 30 euros for electricity and water together.
Hope my review was helpful for you.