A reasonable depth and diameter for postholes dug in clay soil to support an 8′ fence

If you already bought (and can't return) 8 foot wooden posts and you want a 7 foot high fence (or "at least 7 feet") I would suggest not burying them at all, as that's doomed to failure. Put metal post bases (or metal posts) in the ground and bolt your wooden posts to them. Otherwise buy 10 or 12 foot wooden posts if you want 7-8 feet above ground and you want them to stay put. Or, bury them 3-4 feet deep and bolt 2x2 or 2x4 lumber to them aboveground to get to 7 feet (or more) above ground level.

If you didn't already buy them I suggest you learn about metal posts, they are usually much less expensive and easier to set, as well as somewhat safer around livestock than PT wood. But you still need enough post in the ground to hold the post in the air stable, and unless you are drilling holes in solid rock to place your posts in, a 1-7 ratio is dubious in the extreme - and so is placing concrete footings above frost line. In reasonably solid ground an 8 foot post can be driven in 2 feet and leave 6 feet above ground, but your corner posts will definitely need some bracing to stay put, and/or will need to be longer.

Wire (mesh or not) is actually more demanding on the posts than a wooden fence - the wire pulls and provides no support - wooden fence sections provide some bracing to the posts.

Depends on frost depth, height, and strength requirements of fence.

We generally drill 8" holes for a 3.5" square post 6" below frost depth or 30" deep in our area. Minimum depth if frost depth is not an issue I would say is 18" for a heavy clay. Deeper is better than wider. This is for fences upwards of 6' high. Higher fences we would probably set a deeper minimum post depth.

If we had a 120mm round, we would probably stick with the 8" diameter hole, but if it was 120mm square, we might up size to 10" diameter to ensure enough concrete around the post for it to stay intact.

If we needed more lateral strength, we would up size the hole diameter if we did not go any deeper.

For holes that layout cannot be adjusted and are not in the center, we enlarge the hole as needed to make sure there is adequate concrete surrounding the post.