Can a plant survive in only compost ? ? Technically No, a plant needs air, light, ect.
Compost can supply all the nutrients and minerals needed for growth, But is often insufficent due to its heavy nature, Roots need oxygen to survive and compost tends to be to dense for health growth of most species (not all thow).
Compost usually refers to the top few inches of the earth that are mostly broken down ready for the plants to use, or the man made version of that.
When your looking to make your own soil mixes, You first must know the species of plant your growing and its preferences, also factoring in your local growing conditions will help as we all live in different climates.
Best place to start is observing the earth layers around your home and how the plants do in it.
their are also some great youtube videos around, hopefully others can point you in the right direction.
Check out the thread in - Supplyers and resources area --- Soil, Compost, Nutrient Information (offsite links)