Ground wire confusion

[a12548]

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?

[Lightwave]

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.

[hj]

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