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You might be better off allowing it to dry out on a tarp as you suggested and then spreading it throughout the garden.

Using goat manure in the garden is a great idea and will help the soil considerably. You may want to compost it before you spread it to reduce the smell, but other than the smell, you can use it directly. Here is more information on using this type of manure: https://www.gardeningknowhow.com/composting/manures/goat-manure-fertilizer.htm

Manure is great for the soil and plants and there are many types of manure that you can use so finding it shouldn't be difficult. It is normally best to let it age some before use to prevent burning plant roots, as most types are high in nitrogen. You can also mix it in with compost. The manure can then be mixed into the planting soil. Here is more information: https://www.gardeningknowhow.com/composting/manures/the-benefits-of-manure-in-your-garden.htm

It can't hurt to use it. The nutrients make have broken down and be too far gone, but they may not. There is nothing that is in it that will harm you plants and can only help your plants.

This article should help you with that: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/lower-acid-soil.htm