Ground wire confusion

I re-sided my home and will reattach the ground wires back to house. Can I group all 3 ground wires together on clips? Can I use the regular plastic cable clips? They all lead to the hose bib, and they are attached with straps that tighten with a screw. Im replacing hose bib, does Home Depot sell those straps?
Also my new air conditioner seems to have an old ground wire which is loosely clamped to a line coming out of house then leads to just a ground block mounted on the house that ends there, nothing attached to it. I suspect its left over from my old unit, how are units such as Goodman grounded?

From your description it doesn't sound like your grounding is code compliant or particularly safe. House ground wires must be connected to a good quality ground connection--a hose bib doesn't count. At minimum, you'll need a ground rod.

Ask your local electrical inspector what the code requirements are in your area for grounding.

What size are the wires? That connection sounds like an old telephone ground line.