No, in short.
Termites and black ants can actually live side by side in unity. Now don’t get me wrong, because if you were to put a termite and an ant together in close proximity the ant would just pick the Termite up and take it back to the nest and have a little Termite BBQ.
But because Termites are housed within their mud tubing and nests, that tubing is impenetrable by black ants so that is just one of their defences.
So please do not think you are safe because you have black ants.
No, Cockroaches cannot enter your house through the drain as they cannot breathe underwater. They can however come in when you leave a door open and crawl into a drain to hide, then come out at night and it will seem like they are coming out of the drains.
Yes you should get another inspection carried out on your home, and Now!
Australian standard 11.1. STANDARD VISUAL TIMBER PEST INSPECTIONS states that Inspections should be conducted at least annually and, often, more frequently, depending several factors. Mainly the level of risk your house is to termite attack.
All houses Australia wide are susceptible to termite attack and some more than others.
Termite barriers and baiting systems come with warranties that will protect your house in the event of Termite entry.
No, or at least 99% of insurance policies do not and will not cover you in the case that termites have damaged the property..
However, in some cases if you are claiming water damage on the property and you can prove that termites entered because of that moisture you may have a slim chance of assistance from your insurer.