You do not state your age in your profile but your questions show little physics background.
Have you read the wikipedia page on magnets?
North and south poles of a magnet were defined at a time when there was no theory to explain them, but people had observed that some iron rods oriented themselves always towards the north south axis with one side pointing north consistently, so they named the poles. As the link says now one can define the poles by the right hand rule, since one can have a magnetic field from current carrying wires.
In elementary particle experimental studies no magnetic monopoles have been found, not for lack of trying. There does not exist a single north or a single south pole, as one finds with charges.
And, [k]now that I'm thinking about it; are there actually magnets with only a north pole or a south pole (if not, why are the 2 so fundamentally connected that you can't have one without the other)?
No, there do not exist such separated poles, although human ingenuity can simulate such poles by concentrating the magnetic field lines at one pole and geometrically distributing the other field lines so that the field is locally very weak there.
Magnets are at least dipoles . Naturally found iron magnets have tiny dipoles lined up inside to create the macroscopic external magnetic field.
In order for monopoles to play the same role as electrons, as is implied in your question,they would have to exist and be as numerous as electrons. This evidently is not the case as no magnetic monopoles have been observed in all the data up to now. Theories abound, your expectation is a sort of theory, but until there exist data validating the theories we cannot be speaking of monopoles as existing. They are hypothetical particles.
If you want a correspondence with electric charges it is the electric dipoles that are the analogue for the magnetic dipole. Many atoms and molecules have these electric dipole moments they are not as attractive or repulsive as bare electron charges, but still they are important for the structure of matter and its chemical properties.