Variant calling and alignment stats

Question

[nadiabeg.comsats]

Hi. I am using samtools flagstats to see the statistics of my alignment file. It looks something like this: I have 10x genomics reads.

 `575130408 + 0 in total (QC-passed reads + QC-failed reads)
  36759786 + 0 secondary
  0 + 0 supplementary
  114890896 + 0 duplicates
  553257360 + 0 mapped (96.20% : N/A)
  538370622 + 0 paired in sequencing
  269185311 + 0 read1
  269185311 + 0 read2
  365701236 + 0 properly paired (67.93% : N/A)
  505922543 + 0 with itself and mate mapped
  10575031 + 0 singletons (1.96% : N/A)
  82619792 + 0 with mate mapped to a different chr
  67685268 + 0 with mate mapped to a different chr (mapQ>=5)`

And using picard tool after alignment to remove duplicates and getting these statistics.

            446442591 + 0 in total (QC-passed reads + QC-failed reads)
            36759786 + 0 secondary
            0 + 0 supplementary`
            0 + 0 duplicates
            424569543 + 0 mapped (95.10% : N/A)
            409682805 + 0 paired in sequencing
            205395057 + 0 read1
            204287748 + 0 read2
            275640808 + 0 properly paired (67.28% : N/A)
            384153847 + 0 with itself and mate mapped
            3655910 + 0 singletons (0.89% : N/A)
            64548392 + 0 with mate mapped to a different ch
            53575771 + 0 with mate mapped to a different chr (mapQ>=5)

My question is why the number of properly paired reads, and other types drops? Second question is for variant calling is it mandatory to use only properly paired reads? In my case its ~67% which does not seems to be a good percentage.

Best Nadia