No, molecular orbitals and hybrid orbitals are not the same thing. They com from two different bonding theories. Molecular orbitals are linear combinations of atomic orbitals i.e. they come from adding and/or subtracting atomic orbitals. Also, in MO theory you are combining orbitals from two or more different nuclei. Hybrid orbitas are also linear combinations of atomic orbitals but the orbitals that are combined are on the same nucleus. The hybrid orbitals have mor directionality and can overlap with hybrid orbitals or atomic orbitals on another atomic nucleus.
Now, in MO theory you can have s-p mixing. If the s and p orbitals are close in energy (they are in Li-N), the s and p orbitals can mix to become orbitals that look a lot like hybrid orbitals (which for all practicality they are). This changes the energy of the MOs becasue the amount of overlap changes) More overlap means a lower energy.
Yes, all types of orbitals can participate in bonding. s, p, d, f, g, h, ... and so on! d orbitals are often involved when a atome is making more than 4 bonds. Also d and f orbitals can form pi bonds if they are aligned just right. They can also form delta bonds if they are oriented parallel to one another.