Identify Mapped reads and Unmaped Mate pairs

Hey, I have a sorted bam file which i got by mapping with reference. I want to identify two things from this bam file.

1. How many reads mapped to each gene/contig in my bam file.
2. As this was paired-end data, i want to know how many genes/contigs just got a single read out of a pair mapped. like Forward read mapped to contig but reverse didn’t.

I’m trying to find the answers using Pyhton library Pysam.
My Bam file headers are

@HD VN:1.5 SO:coordinate
@SQ SN:TRINITY_DN30590_c0_g2 LN:223
@SQ SN:TRINITY_DN30590_c0_g3 LN:331

and bam file looks like this.

HWI-1KL178:42:c39jdacxx:3:2308:16762:5814/1     16      TRINITY_DN30590_c0_g2   1       9       19S55M27S       *      0                                               0AGGTTTAATTGCAGAAGCTGAGCCTTTCATCTCCATCTTGGGGGTTTCCAGTTCTGCTAGCTGTGCCTCCAAAACACTGGCCTTACTGTATAATTCATCAG   FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIFIIFIIIIIIIFIIIIFFFFFFFFFFBBB   NM:i:0  ms:i:110        AS:i:110        nn:i:0  tp:A:P  cm:i:9  s1:i:46 s2:i:0 de:f:0                                          rl:i:0

I’m trying this Python code:

import pysam
file = pysam.AlignmentFile("AT165.bam", "rb")
for read in file.fetch():
        print(read)
file.close()

Any help will be great. Thank you.