Is it possible to have a screensaver when a fixed time of inactivity of my touchscreen reaches, showing time, weather, temps or something similar? 
I guess this is more a feature of the used touchscreen device/OS running on the device?
What are you running?
Yes if I only want time or weather, but I would rather like to have som more infos from HA to be shown.
Then you would need an app that supports that. Home Assistant is just a website, it can’t run a screensaver on your device. Talk to @Ionut about adding something similar to Ariela.
I think I can get you part of the way to where you want to go. I’m replacing your word screensaver with HA default screen. I have no answer for inactivity but maybe a timer would work.
Here’s my thoughts, set up HA lovelace screen 1 with weather, time & limited HA data. Add a sensor button to go to your screen 2. At that time an automation fires which will bring you back to the default screen after x minutes.
I use a similar technique to reset my card_selection. The default is the weather card, but say I want to see the football team’s schedule. Just a quick look then return to the weather card.
Hope that helps
If you can use the fully kiosk app (Android), you can configure a screen saver URL there.