Monitoring ASA packet loss via SNMP

I did this with a cron script, stores current value in a temp file then next time uses it to calculate bandwidth utilization since last run.

#!/bin/bash

email_address=""
router_ip=""

# 80% BANDWIDTH [ (384000bps) 48,000Bps ] - 20% = 38,400 Bps
alertBW="76800"

lastBWFile="/var/log/ciscoGW.log"
lastBW=`cat $lastBWFile | awk '{print$2}'`
lastTime=`cat $lastBWFile | awk '{print$1}'`

curBW=` snmpget  -c snmap_name -v 1 $router_ip IF-MIB::ifOutOctets.2  | awk '{print$4}'`

let diffBW=$curBW-$lastBW
#echo "Diff BW: $diffBW"
timeNow=`date +%s`
let diffTime=$timeNow-$lastTime
let alertBW=$alertBW*$diffTime

echo "$timeNow $curBW" > $lastBWFile

if [ $diffBW -gt $alertBW ]; then
#       echo "Over limit!"
        echo "Bandwith used over $diffTime seconds: $diffBW" | mail -s "BANDWIDTH OVER LIMIT!!!!" $email_address
fi

Since I was more interested in actual peaks I've since moved to using rrdtool:

#start 15 minutes ago
#end 5 minutes ago since rrdtool queries every 5 minutes 
rrdtool fetch $FROM MAX -s -900 -e -300 

How does the ASA know which range it is responsible for on the Fiber interface?

It doesn't. Your ISP knows (hopefully) that hosts within given sub-net are reachable via the ASA. In case the ASA wouldn't have connected peer (or other proper route to), the ping-pong would begin: ISP sends packet to ASA, and the ASA sends it back by its default route. That's why I'd recommend at least adding static route saying that your assigned subnet is reachable via Null device.

How do I use the addresses from my range?

Plenty of ways actually. For e. g., you can NAT your private IPs to some IP within the subnet. You can subnet it further and connect some hosts to your ASA directly on those IPs.