If any hole that you dig fills with water it suggests that your garden is very low. If that is the case then you can't really condition the soil to help matters, but need to raise it.
There could be all sorts of reasons. A few brown leaves are quite normal at this time of year, but a large amount is not. Did it dry out early in the year? Is it in a small pot that was caught by a hard frost?
Camellias need an acid soil - do you know if your soil is acid?
JI should have been fine. I would leave it where it is and make sure that it doesn't get too wet again. Hopefully, it will put out fresh shoots in time.
Simply pull or dig them up.
It depends - if you have pigeons you may well find that they will cause severe damage to anything leafy.
It may be over-wet - is it in a particularly soggy piece of ground?
I'd wait and see what happens when the water goes down and the rain is over. Most moulds simply shrivel up when the sun hits them, so you may find that the problem solves itself.
Clematis alpina will grow there. It will need tying in, but other that is minimal maintenance as it should only be pruned if it outgrows its space.
Sunny intervals today, and much warmer (14C). I have some fuchsias that may finally get re-potted.