Unity is a 3D engine, you have to do a fair bit of work to get efficient sprites, atlasing, colliders drawing, tilemaps in it. 2D Toolkit does all that nasty stuff for you, so you can concentrate on making your game. What it doesn't do/provide is any game/genre specific stuff - eg. character controllers, etc.
About your issue with physics -
Unity is what limits convex-convex intersections, well actually its limited by Physx which Unity uses, but that limitation is there for performance more than anything else. But no use shifting the blame really - a future version of 2D Toolkit will support complex colliders - i.e. multiple boxes and circles per sprite, letting you create much more complex colliders. This, unlike polygons, is much more efficient to animate. So yeah, polygon colliders are most suitable for background elements - like the hill and spiked platform shown on the asset store page.
Moving sprites without physics - you should go through the basic Unity tutorials. You can move any sprite using transform.position, etc. Its one of the most basic concepts in Unity. There are some really good tutorials to get up to speed with Unity concepts -
http://unity3d.com/learn/tutorials/modulesWe are working on a much more complete tutorial which should help beginners but even for that you will need
some Unity knowledge.