Regarding the repeats, I am interested in finding short reads that had been mapped to more than one distinct positions on the genome. And also which locations has it been mapped to. Is there a tool that already does this?
Some short read aligners will output multiple mapping locations rather than just the best hit. Bowtie 2 will report all alignments of a read with the -a option set. You could look at RazerS 3, which reports all alignments; the paper also has a comparison to other read mappers that can produce multiple alignments.