Osmosis is the diffusion of water.
During diffusion, molecules tend to move from the region of higher concentration to a region of lower concentration of the substance.
The movement of molecules does not stop once equilibrium is reached, however, the net movement is stopped. which means, the number of molecules that moves to the right equals to the number of molecules moving to the left.
Carrier proteins is to help moving molecules from a region of lower concentration to higher concentration. It picks up the molecules and move them to the region needed. This process is involved in active transport.
If the external solution is Hypotonic, it means that it has a higher water potential (also higher water concentration) than the cell inside. Therefore, due to the rules of osmosis, the water will move from the solution to the cell.