Hi Barry,

Congratulations on composting your household food scraps, leaves and grass!  Before you add more nutrients to your garden soil, you should consider a soil test.  I have attached a link to on how to get one.  It is important to do that to make sure you have optimal nutrients to have a successful garden.  

There are various ways to use your finished compost. You can sprinkle compost on top or mix it into your flower and vegetable beds, gently rake compost into tree beds, blend it with potting soil to revitalize indoor plants, or spread it on top of the soil on your lawn as a soil amendment.

Adding compost to your garden helps improve the structure and overall health of your soil. Compost will help the soil retain moisture and will increase your overall earthworm and microbial population, which serve as biological controls against unwanted pests. In addition, compost will provide a slow release of macronutrients, which means that your plantings will get a steady supply of nutrients as needed. 

To answer your second question regarding planting your seeds on top of the mulch of shredded leaves and grass clippings, that wouldn't be my choice.  I do not believe that the leaves and grass has had enough time to break down.  Does it appear that way to you when you look at your garden?  I would plant seeds following directions on the seed packet after removing the mulch.   

Here are some specifics:

Amending Soil - Work 1–2 inches of compost into the top 3–5 inches of soil.

Growing Vegetables - Give your vegetable garden plenty of compost in the fall. Spread several inches of compost on top of the existing bed, then incorporate it into the soil in the springtime. Put a handful of compost in each hole when you’re planting.
Once plants begin to grow quickly, you can add a half-inch layer of compost around the base
of the plants. Provide “heavy feeder” plants such as tomatoes, corn, and squash with 1/2 inch
of compost monthly—this will result in great produce!

Growing Flowers - In the spring, loosen the top few inches of annual and perennial beds and mix in a 1-inch layer of compost. Or in the fall, apply a 1-inch layer of compost as a mulch to protect plant roots from freezing and conserve moisture.

Replenishing Soil In Potted Plants & Window Boxes - Even the best potting soil gets depleted of its nutrients as plants grow. To replenish nutrients, add an inch of compost to potted plants and window boxes twice a year. Or, make your own potting soil using two parts screened compost to one part sand or perlite.

Trees and Shrubs - When planting a new tree, it’s best to work 1/2– 1 inch of compost into the top 2 inches of soil from the trunk of the tree out to the dripline—the outermost parameter of the tree’s canopy.  Compost used in this way serves as a substitute for the layer of organic matter that naturally exists on the forest floor: it provides organic nutrients, reduces moisture loss, and keeps the soil cool.
Don’t add compost to a freshly dug hole when planting a new tree, as applying compost in this way will discourage tree roots from growing beyond the hole.
Apply compost as mulch to trees and shrubs to prevent weeds and to make plants more
drought resistant. Spread up to 2 inches of compost under the tree or shrub out to the drip line (the outermost leaves on a tree) or edge of the bed. This will help reduce moisture loss and stabilize soil temperature.
You can also incorporate compost into the soil once or twice a year to provide organic nutrients. Before adding compost to compacted soils, gently cultivate the soil with a hand tool; this will prevent damage to shallow feeder roots while making nutrients more readily accessible to the trees or shrubs.
Do not place compost or mulch directly against the bark of the tree or shrub or on exposed
woody roots as this could cause rot and invite pests and disease.

Agricultural and Environmental Testing Lab | UVM Extension Cultivating Healthy Communities | The University of Vermont

Improving Garden Soils with Organic Matter, EC 1561 (Oregon State University Extension Service) (uvm.edu)

How to Use Compost in Gardens and Landscapes | OSU Extension Service (oregonstate.edu)

It is nice to be thinking about your garden in February.  Let us know if you have any more questions.  

Happy Gardening!