So with Corsair link, I've run into multiple problems of the same variety as you're describing, multiple times.
I've given up on using it as I've kinda just decided the software is crappy and I can't be bothered to debug it every hour when it stops working.
I had issues with it detecting fan speeds, colouring of the LED on the H100i itself, detecting temperatures.
All sorts.
Imo, Corsair link is terrible and I've completely uninstalled it; given up on trying the change the LED colour on my H100i (the main reason I want link to work).
Sorry I can't give better advice, but thought you might feel better if you're not alone!
As for plugging everything in, you can get USB header splitters, but I've heard there can be issues with addressing.
You're better off waiting for someone who knows what they're talking about to advise on that!
Hope this helps!