It’s sounding like your AC unit as you’ve said. I’d be surprised if it were not blocked so a bit of investigation should show up the problem.
On the windscreen, they often leak and windscreen fitters these days don’t know about the old style, non-bonded windscreens. The 100% seal is to use permanently flexible Butyl Screen Sealer like this stuff
https://rover.ebay.com/rover/0/0/0?mpre=https://www.ebay.co.uk/ulk/itm/222432186094 .
Remove the panel with the grills in between the bonnet and screen then remove the screen. Remove the rubber from the screen and clean it with a Brillo pad in some warm water. Then dry it and apply the sealant. It needs to go all round between the screen and the glass so it oozes out both sides, just enough. A 6mm bead in the root of the rubber channel is about right. Then fit it to the screen and when it’s about ready to fit, run a bead of sealant round the body aperture, sides and top, just where the outside skin begins to curve into the window opening. Leave the base sealant free and refit the glass.