I have a country table that I am using to plot 3 layers using the visualization wizard. I am using CATEGORY for the first layer and BUBBLE for the second. However when I add the third layer with the options available, it can not be distinctly represented. I am using a basic free license. I would like to know if the third layer can be represented distinctly say by using a patter for example.
Your issue doesn't sound like it's related to your account, but your data. Every data layer you bring into the editor, regardless of what your account size is, should be stylable just like any other in your visualization.
If you're not getting the option to style in the editor, take a look at your data. 'the_geom' should represent either a point, line, or polygon and not 'null' or another non lon/lat input. Try going into your tables from the dashboard and only open that data table to see if you can visualize the data there. Most likely, the issue is with a lack of spatial data, or an issue with formatting in the table that's not allowing CartoDB to pick up the lon/lat.