For your first task you will need to add three layers to your base map by making WMS requests to publicly hosted geoservers.
One of the three layers must be a population density layer from the columbia.edu hosted Gridded Population of the World (GPW), v4 found at this link: https://sedac.ciesin.columbia.edu/data/set/gpw-v4-population-density-rev11.
You will need to decide which layer to use, and to write the code to create this layer.
What do we need to do in order to add a new WMS layer to our map?
For a refresher on WMS requests with OpenLayers take a look at their TileWMS Example
After adding the population density layer to your map you will need to add two additional layers using WMS and publicly available geoservers.
You can find additional geoserver map services at: https://sedac.ciesin.columbia.edu/data/sets/browse?
There are many other WMS services you can consume online, but if you want additional WMS layers you will have to research them.