So sorry to hear you have been having such a rough time. Really pleased that you have nice neighbours, which you share interest in hogs with. Good news that there are hogs around again. Nothing like hogs to cheer us all up.
I imagine what your neighbour heard was the courtship circling, during which the females turn round and round huffing – quite loudly, whilst the male circles her. This can sometimes go on for hours, but doesn’t always lead to mating. Hopefully it did on this occasion and you will have some hoglets visiting later on.
The badger is not good news, for the hogs, hopefully it won’t appear again.
The cameras are very easy to set up. If you are worried about what to attach it to, they have webbing straps with them which you can easily attach to posts, trees, or one of mine is attached to a water butt! There are a few topics about them. One recent one was this https://www.hedgehogstreet.org/forums/topic/best-wildlife-camera-to-use/ There have been lots of others at various times.
Good luck. Hope you and the hogs stay safe. Happy hog watching!