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Generally it is best to never use anything other than quads but if you have to or really want to use N-gons or tris, it's best to use them a) in places where they won't be seen or b) in flat areas. But, again, if you are starting out, just don't use them at all until you get a feeling for when they won't lead to issues.
Lulwut?! This isn't true at all, the square grid isn't visible if you smooth shade your mesh.
Yes you can also smooth shade your mesh.
https://www.youtube.com/watch?v=VudCtEtNXbI
https://www.youtube.com/watch?v=ggADPN06mSk
https://www.youtube.com/watch?v=zXsYgRSrNr0
https://www.youtube.com/watch?v=E3ycw3-P7sg
but modeling in quads is a very good practice to keep topology well defined and clear.
The relevance is that good, quad topology will let you use those edge and face loops selection methods. On a triangulated mesh those are not going to work. Just an example of how good topology makes it easier to work with your mesh in various ways.
Loop cuts are kind of similar; you make those with the ctrl + r keys. You can make these wherever you can select a face loop (ctrl + alt + rightclick). You won't be able to add extra geometry via loop cuts to a triangulated mesh.