differential analysis of chip-seq data

It depends on how many samples you have. If you only compare one sample to the second, you can pool and call peaks and then directly calculate RPKM ratios for each peak. It you have more samples, you may want to use IDR to score differential peaks. You may also use packages such as Fseq or HOMER to treat one group as ChIP experiment while the other group as control to call peaks. Alternatively, you could pool all the samples to call peaks, then calculate read counts in each peak for each sample, and then use DESeq2 or other differential tools to calculate significantly different peaks’ significance and effect size.

In a similar question, I recommended that directly comparing called peaks can be somewhat misleading. This topic is addressed in the documentation of the DiffBind R package on Bioconductor, in the "Comparison of occupancy and affinity based analyses" section.

But if you're just looking for genome annotation software, the annotatr package on Bioconductor is pretty useful

1. For sharing, you can test the proportion of overlapping peaks using bedtools intersect or the find.overlap function in GenomicRanges packages in R.
2. What makes more sense is perhaps to merge all the peaks together using bedtools merge, and then count the number of reads/fragments in each peak for each sample using featureCounts. The output of this is a matrix, which is very similar to gene expression results. Then you can do some differential tests on this data.