Can I call from my Smartphone vía WLAN / Internet a mobile phone in a mobile net for free?

I had that on one of my phones
Wi-Fi calling T-Mobile used it.

All the major carriers have WiFi Calling as an option, but not every service plan will actually include it. If your plan does include this, you can enable/disable it through your Settings menu. But if the option isn't included in your plan, there are several, third-party options that apply to most Android phones.
I frequently use Google Hangouts/Hangouts Dialer for WiFi calling (requires a Google Voice phone number, which is also free to obtain). There are also WiFi Calling-focused apps like Viber which does work off of your cellular phone number. The past year or so a number of messaging apps, such as WhatsApp and Signal (my preference), are now including WiFi calling functionality too. The Google Duo app, a video calling app that works over both cellular and WiFi, also recently added voice calling.

Biffos said:

I am not quite sure to understand correctly. So generally you can call a cellular phone in each country from each country with WIFI Calling for free? But both must have the same app, e.g. WhatsApp can call to WhatsApp or Signal to Signal or Google Hangouts to Google Hangouts only? Or not? Or does it work if the called cellular phone does not have any of such apps or is not a Smartphone but a very simple mobile phone without Internet and such? It is very hard to find understandable / reliable information about that.

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OK so there's a lot of mixed services involving different apps and services in that query.
-- No you cannot use WiFi Calling to make free international phone calls. There will still be charges involved, just like when you use a cell phone. The term 'free' when applied to WiFi Calling is more about it doesn't involve your cellular service plan -- you can make all the phone calls you want using WiFi Calling and none of them get applied to your cellular service as everything involves your WiFi connectivity. It's also more of a marketing term as, unless you're using a public WiFi network or one belonging to someone else, when at home you're still paying an ISP for your home broadband.
But getting back to international calling, there is an exception in that apps like Skype can make free international calls but in this particular situation this does require Skype-to-Skype only. So while you can use the Skype app to call any phone, be it a smartphone, or a flip-phone, or a landline phone for free, when it involves international calls there's still a fee involved (which varies by vendor), unless the other party is also using the Skype app.
-- One thing to keep in mind is that WiFi Calling that's either included by your carrier (it's already integrated into your phone by your carrier) or by a third-party app (you install the app yourself) is just another way to make phone calls. It's essentially the same as using the Phone app on your smartphone, but instead of the call going through your cellular service connectivity (the network of cell towers your carrier has in place) it's going through WiFi connectivity (the wireless signal in a home network or business that then goes through a broadband connection). Again, just for clarity, when you use your smartphone to make a WiFi Calling phone call, the recipient does NOT necessarily have to also be using any kind WiFi Calling app, they just need a phone, not matter if it's another smartphone, or an older flip-phone, or a landline phone sitting on desk.
-- Perhaps some of your confusion about having to use WhatsApp-to-WhatsApp, or Signal-to-Signal, or whichever is related to encryption issues. When it involves encryption, than yes you do need to have both parties (you and whomever you're calling) using the same app for the call to be safely encrypted. You cannot have encryption when it involves just one app supports it but the other does not. Otherwise, when you use WiFi Calling it's just a typical, non-encrypted phone call, by far the most common situation.
-- Regarding WeChat, I don't know if the app itself supports WiFi Calling or it's an add-on. As for WhatsApp, maybe this will help:
https://faq.whatsapp.com/en/android/28000016/?category=5245237
Also, be sure to go into your Settings >> Apps >> WhatsApp menu and in 'Permissions' be sure to allow the app to use your 'Contacts'. This allows the app (or whichever messaging you app you prefer to use) to include your contacts list in the app's dialer. Otherwise, instead of just finding and tapping a commonly used contact, you have to type in their number manually on the keypad.
And don't assume every messaging app/service includes support for WiFi Calling (also referred to a VoIP or Voice Over IP). It's really a case by case basis where some apps do while most do not, and those that do may have varying degrees of implementation of services.

Biffos said:

..... To make calls which cause fees does one have to have a special account with WhatsApp or Signal or Google, etc. or are the fees debited from one's carrier (so it would be enough to just be registered at WhatsApp as I am now with my phone number), are they on the phone bill of the carrier? So can one know before one makes a call whether it will cause fees or not?

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It's important to note the distinction between your phone's cellular connectivity and it's WiFi connectivity. While both are wireless signals, they're two different types of wireless signals. They are not interchangeable and each is directly relevant to different sources. Your cellular phone service provides you with cellular connectivity. Your ISP provides you with broadband connectivity (which is what your WiFi has to have). Distinguishing between the two is important because when it does involve something such as international phone calls, you're going to be paying either your cellular carrier or whichever WiFi Calling (aka VoIP or Voice over IP) service you're using. Just using Skype as an example, these are the rates it charges for international phone calls:
https://skype.pchome.com.tw/en/rate/rate.html#
Different services charge different rates so shop around if you do a lot of international calls.

When doing WiFi Calling just be sure you're actually connected to your WiFi and not using mobile data. Otherwise while your cellular carrier may not be charging you for the call itself, it could charge you for mobile data usage (well, that's if you exceed your cap or you've got some sort of unlimited plan). And don't forget, if both of you (you and your over-seas friend/relative) can coordinate it, app to same-app (i.e. WhatsApp to WhatsApp, or Skype to Skype) international calls are free. That's the hurdle most people find to be a problem, finding a time when both parties aren't busy with life in general and the time zone differences.

i use talk a tone

https://play.google.com/store/apps/details?id=com.talkatone.android&hl=en

and it's pretty great.