IT ticketing system

Google provides no facility for this.

There are many systems on GitHub + others you can find in searching.

Many good ones around, both free + premium.

Google Groups' "collaborative inbox" product can potentially be used in this way:
https://www.youtube.com/watch?v=2uzYQIRS0Ks

Here is an overview on setup:
https://support.google.com/a/answer/167430?hl=en

Here's a view into what this looks like:
https://www.youtube.com/watch?v=TBetsTjjBdM

I'm not sure how robust this solution is compared to actual ticketing systems, but it seems like it's worth testing out for your use case.

While I do not like the idea to use Google for any of the data that I care about (I am biased... against Google - most of the times), if I were you, I would use Google Forms.

As you already have mentioned... Google Forms I think you already know what it can do, have you checked this help article? https://gsuite.google.com/learning-center/products/forms/#!/

I'd like to thank everyone who help on this!