Help me understand my Hub Gear bicycle
In order to understand how your gears work, it's probably useful to do a little experimenting own your own.  Since you have a hub gear, switching between gears is very easy. Just move the lever while not pedalling. This is a lot simpler than a derailleur bike which requires you to pedal and takes time for the chain to move between gears.

It will probably be easiest to assess how your gears work if you just stick to a flat surface or a quiet road with a slight incline. 

Put the bike in first gear and pedal for a known distance, such as between two sign posts.  Count the number of pedal revolutions required to get between the two points without any coasting. Now try the same in gear 2 and again in gear 3.  

Gear 1 should take more pedal revolutions than gear 2 to go the same distance, and similarly gear 2 should take more than gear 3 to go the same distance. 

If you don't find the above to be the case, then you should take your bike back to the store you bought it to ensure the gears are indeed working properly.

Gear 1 is the easiest gear and should be used when going up hills. Gear 2 is usually for flat roads, and gear 3 is for if you want to pedal going down hills. As you become a stronger rider you may want to use 3 for flat roads  an may find that 2 is easy enough for some gentle hills.  If you are new to riding, hills will often seem very hard no matter what gear the bike is in. But the more you ride, the easier the hills will be.

Physics does play a huge role is how easy or how hard it is to propel a bike.  Assuming you have relatively smooth tires, even a slight downhill can indeed make pedalling extremely effortless, and almost pointless as the bike will often roll faster than you can spin your feet anyway.  A flat asphalt road can be travelled at 20 km/h at almost the same effort as walking.  An uphill section that doesn't seem much trouble to walk can actually create quite a bit of resistance.  A 5% grade road probably wouldn't trouble most reasonably fit people to walk up, and most car drivers wouldn't even recognize as a hill at all would actually be reasonably difficult for a new cyclist.