(1) I didn't know that PacBio has systematic deletion at homopolymer regions.

Actually as I understand it the errors for PacBio CLR tend to random and not systematic, but the error rates are higher than ONP and are primarily indels. Newer R10 data from Oxford seems to be largely addressing systematic errors with their data, though I suspect with longer homopolymers (8-10 or longer) this may still be an issue

(2) Below is the IGV snapshot image of the region where Pilon introduced 43 bp deletion. Upper is the PacBio read mapping, while the lower is the Illumina read mapping. All PacBio reads were mapped to this region with ~40-45 bp insertion, and some of Illumina reads also showed insertion. PacBio coverages were even across this region, while Illumina mapping showed a noticeable peak. In my opinion, Pilon might have introduced an erroneous long deletion at this region possibly due to wrong mapping. Am I right?

It can sometimes do this, yes, if you run by default more or allow all error correction steps in Pilon like local reassembly. However this may also be something that is sample-dependent; the region you show here where Illumina coverage is higher is actually quite small (hard to read but maybe 10-12bp?), but isn't exactly double the depth if this were a deletion in the entire population. I have seen instances in microbial assemblies like this that appear to be 'hot spots' for indels, which I suspect may be in a subset of the bacteria in the sample.

I normally aim on the conservative side. I iteratively run Pilon adjusted for ploidy, checking the # of correction in the VCF returned, and turn off any option when running Pilon that allows for larger changes, trying relegating correction to small indels and SNPs.