That flue looks rather corroded and leaky. Being a 50’ run, it would seem there must be some shorter route to the exterior. The furnace must have replaced some other original source of heat. Otherwise, there would be a chimney available.
Hopefully their are other HVAC Contractors to call on to make repairs to this system.
The Service Tech. of note, should have to foot the bill and spend the time to make the repairs necessary to bring this system up to safe operating condition, if I’m enterpreting you pics accurately.
I can’t believe any of this work was permitted and/or inspected/approved.
Depends on the size of the vent piping as compared to the equipment manufacturer specifications/recommendations. Longer runs and/or multiple bends generally need an increased direct vent piping size over the minimum (which will be the connection size at the equipment)