It is safe to touch a ground wire as long as there's no short circuit to ground.
In a normal operating electrical system the ground wire is not energized although the ground wire can become energized if the hot wire makes contact with the ground wire or neutral wire.
A breaker is supposed to trip in these cases but it doesn't always happen so you have to be careful.
Even the neutral wire can be touched without getting shocked as long as there's no electrical fault.
You can use any copper wire for grounding but you should mark the copper wire as a ground wire on both ends if you use another color of copper wire other than green or bare wire.
It's best to use either green colored wire or a bare copper wire for grounding for easy detection of the ground wire but other wire can be used as long as it's marked as a ground wire.
The reason why old houses do not have ground wires is because in the old days when the old houses were built there was no electrical code that required a ground wire.
The electrical codes when older houses were built does not require any grounding of the electrical system so they didn't have ground wires.
Houses built before the electrical code changed to include a required ground wire did not need a ground wire so it was not installed.
The electrical wires in those days also didn't even have ground wires like the new wires of today.
The old houses also only used the two prong electrical outlets without ground which were all that was available at the time.
The National Electric Code or NEC did not mandate or require any grounding in all electrical circuits when the older houses were built so many older homes were simply wired without any grounding or ground wires.
The absence of a ground wire is often associated with having 2 prong electrical outlets that only provide a hot and a neutral wire and no grounding path.
Having a lack of grounding wire in the electrical system can pose a safety risk and even more so with modern appliances that have metal casings which can be come energized in case of an electrical fault.
If you live in an house that has no grounding on the outlets and other electrical circuits it's best if possible to get the wiring up to code and install grounding. '
In some cases all you may need to do is upgrade the outlets and install an additional grounding wire.