Based on your clarifying comments, I come to the same conclusion that you have...it's the concrete slab that's the issue. By the sounds of it, it's actually routing water towards your foundation.
I had this exact same problem at my previous house. One side of the house had a concrete slab. Unfortunately, whoever poured it did a terrible job. By the time we purchased the house, the slab was sloped towards the foundation. Someone had previously tried to remedy this by applying a leveling compound on top that was now flaking off. As it was a monolithic slab (and was in MN) it also had huge cracks all over the place.
Whenever we got a severe downpour, we'd get a few puddles in the basement coming in from the footer. I purchased quite a bit of concrete crack repair (caulk) and filled in as many of the cracks as I could and all along the joint between the concrete patio and the foundation. That'd work for a season or two but inevitably the seasonal freeze/thaw cycles would open everything up again and I'd have to get more patch.
As we wanted to finish the basement, the eventual fix was for us to tear out the entire concrete patio and replace it.
I had a team come in with jack hammers and skid steers to remove the slab. I then brought in 4" of crushed rock and compacted the based ensuring I had significant slope AWAY from the house. I then put down 2" of sand, concrete pavers, and polymeric joint sand.
This fixed our water problems completely. I may have overcorrected the slope (the patio was noticeably sloped but I figured it was better safe than sorry. Our eventual paver patio ended up being about 10' out from the house, and slopped probably 8" from one end to the other. Never had water leak in that side of the house again.
Unfortunately, that is neither a cheap nor easy solution, but will say the pavers looked a lot better than the concrete in the end. The primary reason we went with pavers (aside from looks) is that we felt it'd survive the MN winters better and is a whole lot easier to repair if it ever needs to be. While there was a bit of settling here and there and the occasional weed or two you need to pull out of the cracks, for the most part, I was impressed at how maintenance free it was.
Correlation is not causation.
No, the insulation did not make your roof leak around the chimney nor at the vent. Being 100 years old (and odds are great someone did something sketchy during one of those years, though even the best construction/repair jobs don't last forever) did that. Rather than chase chimeras, fix the leaks.
My home was built in 1979, and I have a small leak in the basement. It appears to me that the water is coming from a piece of 1×4 that is embedded in the footer, presumably this wood goes all the way thru to the outside and is now rotten and leaking. As this is the wet season, I'm trying "radonseal" to stop the leak for now, then a more proper fix this summer. I'm thinking I can just dig out the rotten wood and patch with new concrete once things dry out. My question is, why is this piece of wood sticking thru a basement wall in the first place? Maybe it was intended as interior wall then they changed plan? Basement leak 
Best Answer
In the photo there is evidence of two different concrete work. The original is the curb with the 1 x 4 projecting from it and a more recent mix just above it. There is also a visible seam line on the wall which may indicate the wall was opened for some reason. In either case the board was most likely part of the concrete form that was constructed when and if the wall was repaired. My only doubt about it being form work is that it wasn't or couldn't be removed. Unless it was by the previous owner DIY-ing a wall repair.
But I'd agree with your plan to remove it and plug up the opening. If you use hydraulic cement patch you would not need to wait for the opening to dry. In fact hydraulic patch preforms better when the surrounding concrete is slightly wet. It will expand slightly so that it fills voids fairly completely.