Solar panels which are solar photovoltaic (solar - electric), i.e. produce electricity (or convert the solar light energy to electrical) directly usually do have solar cells. Solar cells are the building blocks of the solar electric (photovoltaic) systems.
The solar cell by definition is the smallest technical device that on its own can convert solar light energy in to electricity.
The solar module (hold on for the solar panel definition) is the smallest, most basic component that in addition to being able to convert light to electricity also is environmentally protected and has the physical configuration to be mounted in a useful practical photovoltaic solution. I.e. solar cell, yes, you can use to produce electric energy form sunlight but you can not readily place outside exposed to the elements and conveniently connect to rest of the electric circuit of your system. While modules consist (usually) of cells and are meant to be completely enclosed in proper materials (usually frame and long term sealants) to be protected from the elements and have electric leads out ready to be connected to a standard photovoltaic circuit.
Solar panels are usually the solar modules themselves (in most cases) but the definition for them is that they are also either one module or several, assembled for proper mechanical mounting.
Again in 99% of the cases a module is also a panel - i.e. having both the characteristics of being environmentally isolated and build in a manner ready to be mounted connected to a photovoltaic circuit.
Now when we said modules and panels in most cases consist of cells, what we meant is there are technologies of solar panels/modules in which the cell is not an easily identifiable separate component. This is the the case of all of the kinds of thin-film modules. In them the cells are practically intangible or invisible or at least visibly inseparable and are built as a monolith structure of the panel/module.
Have in mind we started also the answer with saying this is only for solar photovoltaic. Things are very different for solar thermal (electric) and also different for solar thermal (water and air heating).
Yes. A 12 VDC solar panel usually has 36 solar cells inside the panel. Assume about 0.5 to 0.7 vdc per cell.