Project management (PM) includes many different aspects, such as resources (time, people, materials, premises, etc.), but also aspects relating to communication and decisions (e.g. protocols) or documentation of knowledge (e.g. wikis). Other components of PM can also include the following questions: How are tasks sensibly distributed and stored in an accessible way, e.g. with Kanban? How do you organise the sharing of files and set up a folder and project structure that makes sense for the project? 

In the context of game development, mechanics are rules that describe main features. They can describe abilities, but also represent circumstances in the game world and reflect recurring rules of the game. By "core mechanics" we often mean character-defining mechanics for a game. These define the gameplay, the functions or the possible actions of the person playing the game.

An example: In Tetris, a core mechanic of the environment is that new blocks continuously fall onto the playing field in a certain rhythm. The "turning" of the blocks turns out to be a core mechanic for the possible actions. 
 

It is important to estimate the scope of a prototype fairly and with enough buffer time. 
To develop a prototype, you need the resources of time as well as people and their skills. If a game prototype is out of scope; because the idea is too broad, the production team is in danger of overloading itself. The project could fail, for example due to a lack of human resources. This and other problems should be avoided through good scoping.

Paper prototyping describes the process of testing a game concept and its mechanics on paper before going into production. 
The principle is often used in physical table top games (board games), but it also helps in digital game production to physically test with pen and paper whether the concept works or not.You can already test scaling, i.e. proportions, and also mechanics.

Whiteboxing describes a process in which simple white boxes are placed in a level in order to visualise it first. 
This involves building out a level completely with placeholder objects so that everyone involved gets a good spatial idea of the level. Later on, the whiteboxing is then used as a template and can be used to decorate the real level with 3D models or 2D assets.