How to correctly call a VCF file using damaged DNA? (IonTorrent & FFPE)
Sites that were deaminated are often called abasic sites.

Q1: How to obtain DNA damage metrics?

You might want to check out mapDamage - this software is used to perform these sorts of analyses and produce plots of types of DNA damage along sequencing reads.

Q2: How to correct for abasic sites and other DNA damage errors?

You can use your choice of kmer-based or alignment based error correction software. The errors will be random and if the sequencing depth is sufficient the erroneous kmers at the ends of reads will be corrected. However, depending on what you are trying to do downstream with your reads you may be better served by not correcting the reads, then dealing with transitions/damage later.