Hmm, I'm not sure you are likely to get integrations like those (unless Zapier is very keen).
You can see the inventory easily in the Dashboard, and you can export it to a CSV - so not much to be gained for the effort involved. If you did want to automate this task you could write a Python script and run it on your desktop.
With regard to tickets it is probably easier to direct the issues as emails into your ticket system, and have it parse the emails.