Another picture- top view

Roses hate to be inside. Even if you think your kitchen is humid I can assure you it's not humid enough for the rose, nor would you want it to be. Also, all the lamps in the world can not replace natural sunlight. The best thing you can do is put it outside. I don't know about that cactus mix either. Any good quality potting soil would be better for it.

Unfortunately it's already fall weather here in Toronto with temperatures close to 10-15 C (50-60 F). Winds are quite strong too. I'm afraid putting it outside might just kill it even faster. I suppose these are a lost cause? :(

No, they're not a lost cause at all. Can you plant them outside in the ground somewhere? As the weather changes they will go dormant for the winter and should come back even better next spring. Plant them deep, the crown should be about 2 inches below ground, and pile them with leaves or mulch once they become dormant. Minis are usually own root and are pretty tough little cookies. Even if they die back completely to the ground over winter they should come back from the roots in the spring. There are a lot of roses that will survive zone 5 winters with no problems and minis are some of the toughest!

Thanks, Seil! I'll try that.