Are cells spheres or ovals/circles bound by phospholipidbilayer? If they are spherical how are we able to see the nucleus through the phospholipid bilayer under a microscope?
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Not exactly. That is a stereotype of cells. Muscle cells are not round nor oval, but rather elongated rods. If you were to look up epithelia cells, you can quickly see that cells are grouped based on their physical characteristics; simple (round/oval & single layer), columnar, and cuboidal to name a few. Cells come in many shapes and sizes. As Hans stated, stains are vital in viewing cellular components. There is a diverse amount of stains used - which all carry a purpose and benefit in a specific application.
As MG_MD already pointed out, cells come in all shapes and sizes.
Take for example this image of a neuron. The central cell body contains the nucleus and is surrounded by a network of extensions called neurites which form neural networks. The extensions and the cell body have been stained fluorescently to make the cytoskeleton visible:
The reason why we are able to see inside them is because the plasma membrane (a phospholipid bilayer) is transparent. Check out this website for some nice movies of cells moving under the microscope. In the left of these movie (keratocytes) you can clearly see that the cells have a bulge where the nucleus is which is surrounded by a flat so called lamellipodium giving the cell and overall "fried-egg"-like shape.
The only time when most cell types are rounded is during cell division. This is to make sure that the cells divide evenly and each daughter cell gets an exact copy of the DNA.