I've been riding all winter on HardCase Lite R3 tires that came on a Trek I bought last fall with zero flats for 2200+ miles, and I've sure liked the zero flat part as well. I don't ride in the mountains in winter so I figured I'd beat em up on bad roads and see how it went. Didn't care so much about performance off season and they've served their purpose. No, they're not supple and I wouldn't want to ride anything challenging at all on them and I'll lose them going into summer. I had similar tires on a different Trek a few years ago and knew on my first ride down a mountain they had to go straight away. So anyway I have recent experience with similar tires
You're gonna flat more regularly. Period. I usually ride GP5s in winter and don't get many but some
Pretty sure your tires are around twice as heavy as a better performing choice, so you'll immediately lose about a pound from your wheels. It's gonna feel different and better whether or not you're faster, and it'll handle way better when you need it
I replaced my last stock wheels because they weren't stiff enough for me, but I'm going to replace the ones on the new Trek because they're just too heavy and narrow. Unsure about the faster part, but if you go aero they'll definitely look cooler