The icon at the left bottom corner of my windoews ten programme does not react when I click on it. It only works when I right click on it but tha does not give me the list of programms. The same goes for the icons at the right bottom corner.

There will be some bugs in your Windows 10 because it never happened to me. I think you should check for updates for your windows 10 but not to go with insider or beta program because it may cause some major bugs as it's already written on their T&C so go with regular updates and this problem will definitely fix your bug.

I don't see the problem here. Apps can sit in the tray and depending on the app's coding either do nothing on a click or a right click. What you want it to do has no bearing on what happens.

If you are trying to identify what it is, you can examine your PC with tools like AUTORUNS, Hijackthis and other tools. It takes time to know your PC and if you think it's a trojan then I'd post (read THE RULES) at bleepingcomputer.com.