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It does not matter whether peat or manure go in first as they are all worked into the soil evenly.

Here is an article on sandy soil amendments that will help you:
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/amending-sandy-soil.htm

I think this depends more on the type of charcoal used. If it's natural wood charcoal then it's okay to put the ashes in your compost or mixed in with the soil of your garden. If it is the type that has additives (chemicals), including lighter fluid, then I wouldn't use it in garden or even compost. Check the ingredients and the label. Also, be sure to let it sit for several months to age before using on plants when putting the ashes in the compost. Here is more information: https://www.gardeningknowhow.com/composting/ingredients/wood-ashes-compost.htm
https://www.gardeningknowhow.com/composting/ingredients/composting-ashes.htm

As long as they have been sitting awhile (a year should be sufficient), then I don't see why this should pose a problem, though mixing with compost may be better.

You will need to check with a local rose society to find out the best time to plant a climbing rosebush there, I plant rosebushes very early in the spring here in Colorado which is mid May typically to early June. I prefer using the shredded wood mulch as the peat mosses can carry some funguses and molds that will spread disease to the roses and can actually cause us gardeners some issues as well. https://www.gardeningknowhow.com/ornamental/flowers/roses/rose-pickers-disease.htm

Yes, Annual Ryegrass can be planted as a cover crop.
Here are some links with more information.

http://covercrops.cals.cornell.edu/annual-ryegrass.php
http://www.mccc.msu.edu/states/Ohio/OH_CoverCrops_to_Improve_Soi&Water_Quality.pdf

It would probably be ok since you are planning on tilling it all up, though I think adding them to the compost pile might be better. In a compost pile, you would be adding additional items to help balance out all that acidity. You may want to test the soil first should you decide to put them directly into the garden to make sure the area isn't already too acidic, which would not be a good thing. But a soil test would at least let you know what other nutrients, if any, need to be added so you can take care of it at one time.