@anique.yael, a lot depends on what you use the document for.
In the interest of transferability, I guess I would propose a proper instructable. Spreadsheet (i.e. database-like) documentation encodes the world view of the person designing the database (i.e. creating an naming the columns). "Internal/external" and "how to/materials" may seem obvious to you, but obscure to someone else. The instructable format assumes that the reader has no idea what the writer is talking about, so the latter needs to make an effort to take no prior knowledge for granted. The additional advantage of a good instructable is that it becomes another part of the digital commons: people outside ER can use it too.
I like your idea of dividing the work into phases, it's quite natural. So, the phase "from successful application to grant agreement" could become a wiki. "First: update beneficiary details. To do this, do the following: [...]". So could other phases, etc.
This for the documentation. For the project management side, we could even imagine a Dynalist: every time we win a project, we duplicate a whole set of tasks. But, again, Dynalist will only be viable if and when we have email notifs.