There is no "one fits all" language, therefore I would simply use multiple lanaguages for that project:
Frontend: if it has to run on iOS, Android, browser and Desktop, I would probably go with apache cordova here and use web technology (i.e. js, html and css, maybe webasm). Here you could also use Lazarus with pas2js.
Server backend: Here I would probably use Lazarus, C++ or Java, depending on the specific needs. I really like writing server protocols in Pascal, but if you need to use an already established protocol, chances are good that in java it will be only one maven dependency and 10 lines of code
Neural net: Defenetly python, no question, the amount of information about Torch, TensorFlow, etc. on the web is pretty good for python, and even if there are also bindings to many other languages, you don't find much information about it.
And for your specific points:
Good adaptivity to screen sizes;
Javascript and webtechnology
Scrape information from the web;
I've had good experiences with java and python in that regard. Python scripts will be shorter, but to be honest I really like Java because of it's simplicity and robustness
Get additional information from users all over the world;
Server architecture that I would write in Pascal, probably using HTTP (because it's easy) and communicating with a decentralized Mariadb backend.
Prepare this information for use in a neural network;
I would suggest that the backend server chooses a sensible intermediate format, and the processing for the NN would than be done in the language chosen for the NN (probably python) because changes in the NN should not require changes in the backend.
Use this information in a neural network (preferably peer to peer redundantly distributed);
Python with pytorch
Us the results for actions on the internet (connecting to API’s running on 3rd party servers);
Also doable with python, but also possible with any other language
Us the results for actions on user devices;
Frontend -> JS
Off-line first where possible (using PouchDB?);
If you want to use PouchDB you need JS, otherwise there is the Java version of this CouchDB. If you want to use certain tools, this often takes the language decision for you
Fast UI, fast reliable communication, fast response from neural net, even on mobile phones;
Javascript is great for UI, reliable communication is possible with every language, and fast response from the NN is dependend on your NN, if its a large network and you don't have a great GPU (like Phones) it will take long. My suggestion, do the NN stuff on the server side and not on the phone, because large networks take time, simple as that.
Fiercely secured against attempts to disrupt data collection, -communication and -processing;
Use a CDN for your backend, this is completely language independend
Automated backup facility if so needed (Central, distributed, hybrid; Whatever would be best; It’s open for suggestions).
This is also language independend
About your questions:
Question 1:
Nowadays React Native is used a lot for Cross Platform Mobile Apps.
Can Pascal use React Native or even do better itself? When yes then how?
React native is basically just a javascript interpreter that grants access to system APIs to javascript via a framework. It is built for javascript and has no interface for other languages (afaik).
Question 2:
The best property of Smalltalk is live coding (REPL).
Can this also be done with Pascal? When yes then how?
Live coding is a bit against the spirit of a compiled language, and I don't think it would work that great with pascal, where you have to write a lot of boiler plate code before anything can happen
Question 3:
Microsoft is open sourcing the .net framework.
Can Pascal use the open source .net framework or even do better? When yes then how?
.Not uses a bytecode language that runs in a sort of VM. It is not compatible with assembly. While on windows there are possibilities to use .Not DLLs with native code, I don't know if it is portable at all. So the conservative answer is a "maybe but probably not"
Question 5:
What role can Lazarus play in all this?
Or would VS-code be a better option for certain needs?
Lazarus is great for Fpc-Pascal, simple as that. If you want to use any other language or any other compiler (like Delphi) it's probably better to use a different environment. For example, for Pyhton and C++ I really like Emacs, for JS or C# VS-Code is really great, for Java I'd go with Intellij.
So to summarize, I would use different languages for different needs, simple as as that. Every language has it's pros and cons and to do everything with only one language will only make your life harder
PS: Whenever I write JS I personally would use Typescipt, because I'm not an insane person. But it's compatibility is bascially the same