Whenever you like or whenever the product is available. There isn't exactly a "bad" time to add compost or composted manures. I use compost as a general mulch in fall (and again in spring, if necessary) but if you are using it to improve existing soil conditions (like adding nutrients back to a vegetable garden), then incorporate into the planting area a couple of weeks before planting.

Fall is fine, you can either dig it in or lay it on top and cover it with leaves, grass clippings etc. for winter. It's a buffet for the worms.

It kind of depends on your soil and how much other organic matter is there. In sandy soils with little organic matter the nutrients that manure has could be washed out of the soil if applied in the fall before any plants could utilize them. If applied in the spring, and that spring is quite wet, the same thing could happen while waiting for the seeds to germinate.

Manure can be a could addition to any soil but it needs vegetative waste in the soil to hold the nutrients where they are needed by the plants. There also is no "proper" time to apply composted manure which can be added to soil anytime. Fresh manure should not be added to soils when plants are growing, however.

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