No it can't do that. It's an LLM, it can only generate the next word in a sequence.
Your knowledge is out of date, friend. These days you can configure an LLM to run tools like curl, nmap, ping, or even write then execute shell scripts and Python (though, in a sandbox for security).
Some tools that help you manage the models are preconfigured to make it easy for them to search the web on your behalf. I wouldn't be surprised if there's a whole ecosystem of AI tools just for searching the web that will emerge soon.
What Mozilla is implementing in Firefox will likely start with cloud-based services but eventually it'll just be using local models, running on your PC. Then all those specialized AI search tools will become less popular as Firefox's built-in features end up being "good enough".
AI models aren't trained on anything "stolen". When you steal something, the original owner doesn't have it anymore. That's not being pedantic, it's the truth.
Also, if you actually understand how AI training works, you wouldn't even use this sort of analogy in the first place. It's so wrong it's like describing a Flintstones car and saying that's how automobiles work.
Let's say you wrote a book and I used it as part of my AI model (LLM) training set. As my code processes your novel, token-by-token (not word-by-word!), it'll increase or decrease a floating point value by something like 0.001. That's it. That's all that's happening.
To a layman, that makes no sense whatever but it's the truth. How can a huge list of floating point values be used to generate semi-intelligent text? That's the actually really fucking complicated part.
Before you can even use a model you need to tokenize the prompt and then perform an inference step which then gets processed a zillion ways before that .safetensors file (which is the AI model) gets used at all.
When an AI model is outputting text, it's using a random number generator in conjunction with a word prediction algorithm that's based on the floating point values inside the model. It doesn't even "copy" anything. It's literally built upon the back of an RNG!
If an LLM successfully copies something via it's model that is just random chance. The more copies of something that went into its training, the higher the chance of it happening (and that's considered a bug, not a feature).
There's also a problem that can occur on the opposite end: When a single set of tokens gets associated with just one tiny bit of the training set. That's how you can get it to output the same thing relatively consistently when given the same prompt (associated with that set of tokens). This is also considered a bug and AI researchers are always trying to find ways to prevent this sort of thing from happening.