You can add the lime anytime to bring up the ph. Agricultural lime is ground limestone, and will not injure the plant roots even if sprinkled directly on them. It is slow dissolving and so will take some time to work. Do it now.

Amending with compost should be done only when first planted and during the growing season. Why waste that wonderful compost on dormant plants? You can use compost on your still growing garden and expect some result. But if your garden has really failed, and you don't intend to plant more veggies, save the compost till next year.

I'm a believer in green manure crops to improve soil tilth and fertility. It really works the same as composting, but is used over the entire space. I would sprinkle some buckwheat seed and lightly rake it in to the top 1/2 inch. It will sprout in 3-5 days, and in about 5 weeks you can till it in, or hoe it into the soil. That's a quick fix for this year.

In the fall, Sept. or early Oct. sprinkle some winter rye seed and rake that in. It will sprout and hold the soil over the winter. In the spring it will start to grow and I usually till that in when it's about a foot tall.

That will add more organic matter to your soil than the amount of compost you can make. Next year when you plant your crops, only use the compost within the row, or directly on each plant, like tomato plants. That way you're not waisting compost between rows.

Do the green manure thing as often as you can. I can get two seedings of buckwheat in one season, if I'm not using the area for anything else. At the very least do the winter rye planting each fall. That will go a long way to improving your soil.

My motto, feed the soil, and the soil will feed your plants.

You can top dress with compost and I don't believe myself that it is a waste to do so when the plants are dormant. It still does add a wonderful amendment to your soil. Yes, feed the soil and it will feed the plants. But adding some compost once a year, either in spring or fall, just helps your soil and is NEVER a waste! Just my opinion :)

This fall, pile some layers of organic material on the garden areas - and yes, 3-6 inches to start is not excessive. Use the compost bins, raked leaves, whatever you can find.

Let it sit all winter and dig it in with more lime in the spring.

If you don't have enough materials for generous amendment, do a smaller area thoroughly instead of a big area with tiny amounts.

If your soil's low in magnesium, you could use dolomite, which increases alkalinity whilst adding mag.
Plant legumes like lupins and favas mixed in with whatever else you feel like. The trick is to cut them down before they set seed. Just leave on the bed. I mulch heavily straight away, but that may not be appropriate for your climate.
At my place, space is tight, so when compost's ready (or not, sometimes...), it goes on the garden. As far as I know, it doesn't hurt to store it, but I'd spread it, put your cover crop in, and get more going.

When to amend soil depends on when that soil needs those amendments. Many of us will amed our soils in the fall as we put the gardens to bed for the winter so they are ready to plant next spring. Keep in mind that it always takes some time for organic amendments to become available, which is why working stuff into the soil in the spring does not always show expected improvement that same year.
1. You need to apply as much compost as your soil needs. That might be 3 to 6 inches once and then much less in the future. It depends on what your soil needs.
2. Compost, added in the fall, will be more ready to your plants next spring. If your Soil Food Web is not very active now they will be more active in the srping because they have something to encourage them to go to work.
3. Now, yesterday, tomorrow, when ever you have the material and time.
The nutrients in compost, if it is kept fairly dry, are quite stable. If bacterial activity in the compsot ios slowed down, by lowering the moisture they need to function, compost can be stored for quite some time. However if that compost is moist enough to allow the bacteria to keep working they will continue to digest that compost and eventually leave you with nothing to use.

Mulch all summer long
and add your compost in fall.
Amend but don't till.

Some clay soils are on the wet side in springtime so much amending is better in fall when the soil is dryer for clay.

I know it's not what you meant, but when I see a question like this, I always think that the answer should be that I amend during the daytime so I can see what I'm doing. But if you have enough light, you could amend at night, also.

I make an enormous amount of compost (grass clippings, horse manure, kitchen scraps, wood ash, etc). I wouldn't have enough room to keep three piles cooking unless I constantly amended my soils throughout the summer and fall.