The main reason one creates a copper zone on any PCB is to get low impedance current return paths without needing to think about it too much. (If you don't have a ground plane you would need to ensure to give the current a return path near to the signal to get the same result.)
For this reason one would aim to have an uninterrupted ground plane on some copper layer (In most cases one of the inside layers of a multi layer board is used for this. As the outer layers are already used for signals in most pcbs. A pcb like yours where all signals can fit on one layer is really rare.) Every GND connection is then connected using vias to this plane. (Example the ground contact of decoupling caps is connected in the shortest way possible using a via. This via will be very near the pad. Depending on manufacturing technique it can even be inside the pad.)
We can not answer the question "does my pcb need a ground plane" from a screenshot of the pcb. We do not know enough about the application. (What is the function of the PCB? What type of signals are there? Does it need to adhere to some EMC standard? ...)
SMD parts are mostly placed on one side for manufacturing reasons. (Typically the top side of the design program is used for this.)
Reflow soldering is a lot easier if all SMD components are on the same side. It is possible to have components on the bottom during reflow but this will be more expensive. Some larger components might even need adhesive if they are on the bottom during reflow.