How and why the magnetic field is produced or created in a current carrying conductor?
And why can’t we isolate a magnet?
There are two type of facts in nature, one is called fundamental and others are explained on the basis of fundamentals. That’s why every “Why” don’t have answer in the way we think of. consider someone asks the question “Why electron repels an other electron? “. And the clear answer is due to charge. But if someone asks “Why electron have charge?”, it have no explanation, we say it is fundamental. Hope you understand what I want to say.
Now, answer to your question is based on a fundamental fact :
A moving charge creates magnetic field.
This is the actual origin of magnets. Talking about current carrying conductor, It’s like river of electrons i.e. electrons are drifting through conductor. And electrons possess charge. That means a current carrying conductor is full of moving charges. So these moving charges create magnetic field around the conductor.
This answers your first question. And this also gives a hint about your second question, “Why can’t we isolate a magnet?”.
Even natural magnets have magnetic properties due to moving charges, the electrons spinning and revolving inside atom. So even at smallest level it have complete magnet, consisting of both poles.