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Yes, and you can compost the brambles, too! With correct composting, any seeds will be destroyed. Cut them up for the best results.

Here is a good composting guide that will help:

https://www.gardeningknowhow.com/composting/basics/ultimate-beginners-guide-composting.htm

Unless you turn the composter often enough and have the proper ingredients, it won't get hot enough to kill insect pests. I would recommend removing the stems with mealybugs on them. In the future, watch for any infested plant material and throw it in the trash rather than the composter. A few bugs that don't harm plants are OK, but mealybugs are sapsuckers that will harm plants if they survive the compost bin and are applied beneath plants.

https://www.gardeningknowhow.com/composting/basics/compost-pest-control.htm

I believe you are asking about finding scraps of metal and plastic in your oak leaf compost that you retrieved from a public source. My suggestion is to remove the compost and start over with something fresh. I would also contact the agency or source of the compost to report the problem. It would take years for these materials to break down in the soil, so it's probably best to remove them altogether.

Here's a good article on composting: https://www.gardeningknowhow.com/composting/basics/composting-basics.htm

Unfortunately, for the home composter it is too dangerous to keep these things around. Animal remains can carry diseases that will not compost properly. This means that it may end up in your body at some point.

In nature, outside of a closed system, there are microbes and animals that make quick work of animal skin, meat, and fat. Usually, the only thing left to compost will be bones. It is acceptable to compost thoroughly dried bones.

Unfortunately, the landfill is the best option, unless you throw your scraps outside for scavengers to have a snack. That is an option, also!

The best thing about moldy food in the compost is that it's already begun the decomposition process. It's fine to add moldy tea. Here's a good article about adding tea to compost: https://www.gardeningknowhow.com/composting/ingredients/composting-tea-bags.htm

I don't see it becoming a problem, as long as it doesn't smell bad. 58F, however, will be way too low of a temperature to ferment anything. A little closer to room temperature will be better, but upwards of around 100F will speed up fermentation. I don't see a real need to ferment compost tea too heavily, though.

I definitely wouldn't spray your plant's leaves with anything syrup-like in consistency, though. It is likely to clog the plant up, preventing respiration.

It sounds like you have something still usable as a fertilizer supplement. Just use according to the recipe that you have found.

In the future, these articles will help you to make compost tea:

https://www.gardeningknowhow.com/composting/basics/compost-tea.htm

https://www.gardeningknowhow.com/composting/basics/tips-using-compost-tea-on-plants.htm