Until 'others' follow-up ywith some answers to your question, I think you'd better not use the stove.
I wonder if your instructions 'mention' the word INSPECTION. I know you want to save $$$ but I don't think you can just 'connect' to an existing 'stack' that use to be used by used by another heating 'source'. And if you can, I'm SURE there are safety issues. I think you're experiencing one right now. The cement isn't rated for the extreme high temps. of a wood burning stove, and might be rated for lower temps.
Just as an aside, when my folks installed a wood stove in the living room (it was a free-standing stove; not an insert), they were required to build a separate chimney for it, which they did right NEXT to the one for the gase furnace. Yes, the gas furnace was used for venting a HWH.
Stay tuned! I'm sure others will have more to say.