What are the molecules in the plasma membrane that provide basic membrane structure, cell identity, and membrane fluidity?

These molecules are known as phospholipids (2 fatty acid "tails" with a phosphate group "head"). Because of their charge, the phosphate groups are hydrophilic (attracted to / mix with water) while the fatty acid "tails" are hydrophobic (repel / do not mix with water), which causes them to form phospholipid bilayers.

A phospholipid bilayer makes up each cell's plasma membrane; the hydrophilic "heads" of each cell face the water-containing interiors and exteriors, while the hydrophobic "tails" face one another.

Furthermore, proteins that support cell function and act as channel proteins, protein pumps, receptors, etc. may be embedded in the plasma membrane.

I hope this is useful.

Phospholipids are the molecules in the plasma membrane that give the membrane its fundamental structure, cell identity, and fluidity.