Q:

What is a Polygon file, a PBF, and a Style

I'm trying to wrap my head around what all it takes to create a map tile server. 
I'm following the directions from here: https://switch2osm.org/serving-tiles/manually-building-a-tile-server-14-04/
But, I want to know exactly what's going on. 
What EXACTLY is in the .pbf file? Can I assume it contains all of the roads, borders, lakes, ponds, etc inside of each polygon? And having said that, what is the "polygon"? It wants me to download from here: http://openstreetmapdata.com/data/land-polygons
Is this the shape of continents, etc? 
And how do I create my own style? It suggests using OSMBright, but what if I want something a little different... maybe say like an old-timey map style? 
Also, it seems that those "projections" are all in 3857, the system for which I am building this map server lies in a closed-system that has layers that are projected using 4326, how would I "convert", if that's the correct term? 

A:

Basically, the pbf file contains all OpenstreetMap data inside the given extent (whole planet or less).
The land polygons (aka coastlines) are needed for low-zoom rendering, and to make sure that no data clipping makes your area of interest flooded by the ocean.
Making your own style is easy when you have successfully rendered your first map tiles. Just change the style sheet, and see how changes are visible.
Rendering in EPSG:4326 is also possible (though I have not done it yet). During import of the data, you can specify if the data should be reprojected to EPSG:3857 or not.

