While not exactly the answer to your questions, problems of a similar nature ("how to most efficiently use a space for some or multiple purposes") can be solved using Golomb rulers [1]. I first learned about them when I played with the Distributed.net client to calculate optimal Golomb rulers. I feel they or a similar class of tools can be used as the answer to your questions.

[1] https://en.m.wikipedia.org/wiki/Golomb_ruler