Hi,
A coordinate sorted bam file is required (samtools sort). Quality score recalibration or local indel realignment is not required but it is also not harmful. If duplicates are marked, Delly ignores them but Delly also filters duplicates internally so it is again not required.
Delly should be fairly robust regarding the specific aligner that was used as long as they follow the SAM specification. We never benchmarked which aligner works best with Delly so I cannot really give a recommendation here. Internally we mostly used it with bwa aln, bwa mem and eland alignments.
Best, Tobias