Yes, the missing hose will reduce blower pressure.
I would first get your vacuum lines situation straightened. Changing all the lines may be a bit of overkill. There are a lot of them. Try to isolate the problem area using a vacuum gauge so you can see where you have full manifold vacuum and where it's reduced. You can pinch off tributaries while watching the gauge to see if the vacuum level responds to pinching off one line to isolate where the leak is. If you find some line that just keeps breaking, then replace that section.
Once you have those problems fixed, get the car up to operating temp and feel the temp of both heater hoses. If they are both hot to the touch, then you have an internal blend door problem. If one hose is hotter than the other, then you have a plugged heater core and it will have to be replaced.
78 Corvette Pace Car For Sale-18k mi orig-Florida