Can electrons switch their spin direction?

The electrons have definite spin in the sense that it is always spin-1/2. Such a spin can be in two-states, commonly referred to as up and down states. Normally, the majority of spins will be in whatever of these states that has lower energy (which is usually taken to be the down state), given the applied magnetic field. The transitions between two states can be induces like transitions between any two quantum states by irradiating with light (in the case of spin it is more often microwave radiation) at a frequency matching the difference between the two energy levels, i.e. $$ hbaromega = E_{up} - E_{down} $$ The ability to cause such resonant transitions in protons is widely used in NMR (nuclear magnetic resonance) spectroscopy, which for publicity reasons was renamed into MRI (magnetic resonance imaging) - so that it doe snot ahve word nuclear in it. The spectroscopy of electron spins goes under the name ESR (electron spin resonance).

Not all electrons in molecules are paired with an electron of opposite spin. It is possible for a molecule to have a lone unpaired electron. Since pairing of electrons with opposite spins is energetically favourable, molecules with an unpaired valence electron tend to be more reactive than those without, and in organic chemistry they are known as radicals.

In a powerful magnetic field an unpaired electron in a radical can occupy one of two energy levels, depending on whether its spin is aligned with the field or is antiparallel to the field. An unpaired electron in the lower energy level can then absorb a microwave photon (if it has the correct energy/frequency) and flip to the higher energy level. Absorption of microwave energy by unpaired electrons in a magnetic field is the basis of electron paramagnetic resonance or EPR. EPR is the equivalent of MRI, but applied to electrons instead of photons.