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As long as it is well aged and composted in a "hot" compost pile, it is fine. Otherwise it may have weed seeds in it, depending on what the animal ate. Do not use any manure that isn't fully composted! Check out this webpage on horse manure. Notice the links at the top, including how to tell if the manure is ready for garden use. http://whatcom.wsu.edu/ag/compost/horsecompost.htm

I recommend removing the weeds as much as possible, and covering the area with a black plastic material to kill off any seeds over the winter. Another way to help would be to plant things like clover, peas, beans, or any other legumes, as they add nitrogen to the soil. Here is an article that will help:https://www.gardeningknowhow.com/garden-how-to/projects/how-to-solarize-garden-beds-to-eliminate-garden-pests-in-the-soil.htm

I would recommend fully composting this before adding it to the garden. There will be alcohol content, but not for long at all. It has a very fast evaporation time and will leave the mixture fairly quickly.

This collection of articles will give you some very useful tips on composting: https://www.gardeningknowhow.com/composting

Slugs and snails are the number one enemy of many gardeners and some people believe the compost bin is a hothouse for slug and snail reproductive activity, creating massive populations that will invade the garden and devour the precious plants. Slugs and snails are decomposer organisms that help break down the organic matter in the compost bin so the bin acts as a great feeding ground for them. There is no guarantee that the slugs and snails will not be tempted to other areas of your garden, but the compost heap provides them with an ideal habitat they have no reason to leave as they have a constant food source and are protected from predators - they keep moving up the bin to get to the fresh material, and eventually die of old age.

The short answer is that using paper and ink in compost is generally considered safe. But this is still a somewhat controversial issue with several factors to consider.
Modern printing ink is generally considered non-toxic, but not all reviewer opinions take into account all aspects of the oils used, GMO soy crops, percentage of petroleum oil content and heavy metals that may be present. From what I have gathered in reviewing the published information, Organic purists say no, but there is a lot of opinion out there that says ok no problem.
Here are some articles that may help you decide for yourself.
https://www.the-compost-gardener.com/-composting-paper-is-it-safe-.html

https://www.gardeningknowhow.com/composting/ingredients/composting-newspaper.htm

https://grist.org/article/umbra-papercompost/

https://www.planetnatural.com/composting-paper/

There is no real sequence to adding. You will be mixing all of this up occasionally, and when you first get it set anyway.

There is a less effective, but less hands on way to compost in a "lasagna" fashion. This method requires layering materials, and will not require much maintenance, but there is a lot to be said about a well mixed, and maintained compost pile.

This article will help you with lasagna style composting: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/lasagna-gardening.htm

This article is a well rounded composting guide that will, also, give you many good tips to help you make the best of your compost: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/lasagna-gardening.htm