Another great question, with a lot that could be included in an answer. So my short answers are:
A lot more than most people probably think, and yes!
The first thing to talk about is the earths magnetic field. The whole earth produces a magnetic field, like a giant magnet. It’s how compasses are able to tell you which way North is. It is also generally considered that the earth would not be able to support life without its magnetic field, as it maintains liquid water on earth. It also helps to protect the earth from solar wind.
Some animals are able to detect the earths magnetic field – as if they have built in compasses. This helps them navigate, especially during migration.
The next thing to mention is the relationship between magnetism and electricity. The two are fundamentally linked through Einsteins special relativity. So no magnetism would mean no electricity, which would be pretty significant!
The next part of your question about what magnetic fields can affect needs some explanation of different materials magnetic properties…
The one you’ll be most familiar with is “ferromagnetic” materials. These are the ones that magnets are made of and that are easily attracted to magnets. Their electrons maintain their orientation after they have been aligned by a magnet, and therefore they continue to behave as a magnet whilst they are below a certain temperature. This temperature varies for different materials and is called the “Curie” temperature.
Then there are materials that are “paramagnetic”. These are only affected whilst they are in a magnetic field. So they are attracted to the magnet (not usually as strongly as “ferromagnetic” materials) but they will not remain magnetised when it is removed.
Finally all materials have some “diamagnetic” properties. This is a tendency to be repelled by magnetic fields. This is a very weak force though and is overwhelmed by the attraction force in ferro- and para-magnetic materials. Although this is a really weak force it is present in everything, so can do some really cool things, like make living things levitate above really strong magnets. Here is a live frog floating over a magnet:
So in summary, everything is magnetic in some way, and magnetic fields do have an effect on our life, most importantly we wouldn’t be here without them! There has been some scientific investigation into whether peoples behaviour and health is affected by magnetic fields, but I don’t think anything conclusive has been found.