How to make edge length to always be multiple of a certain number? I want to make a model whose edges' length (all of them) are always multiples of a certain number.

Later on I want to apply a pixel-art texture and I need to have a 1:1 relationship between the texture and the model so there is consistency in the size of the pixel across all faces on the model.
You can use the snapping features and align all your vertices to the grid. 
If your edges are not aligned to the grid you can set the edge length in different ways like described here.