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Keeping this in consideration, what is a subcellular structure?

A subcellular structure is simply structures within a cell. Subcellular structures can only be seen by an electron microscope, either SEM or TEM microscopy. Examples of subcellular structures are organelles ("little organs")- Golgi apparatus, smooth+rough endoplasmic reticulum, nucleus and mitochondria.

Also, is the cytoplasm an organelle? Cytoplasm is not an organelle. This is simply a generic term that describes everything within the plasma membrane and outside the nucleus. We typically think of organelles as being within cells.

Then, what is the structure of cytoplasm?

Cytoplasm consists of all of the contents outside of the nucleus and enclosed within the cell membrane of a cell. It is clear in color and has a gel-like appearance. Cytoplasm is composed mainly of water but also contains enzymes, salts, organelles, and various organic molecules.

Does cytoplasm contain DNA?

Deoxyribonucleic Acid (DNA) is found mainly in the nucleus of the cell, while Ribonucleic Acid (RNA) is found mainly in the cytoplasm of the cell although it is usually synthesized in the nucleus.