Where did you hear this? A particle travelling at c can have any energy, but can have no mass. (E=pc)
I think that this is a bad interpretation of the physics involved. One can not assign a co-moving reference frame to a particle at c, as c must always be c from every frame. Hence, no proper time can be defined (proper time is time as seen from a certain reference frame). This is not due to lack of energy.
Strings are quantum objects, and as such classical physical concepts of energy don't apply to them. Energy becomes an operator (as does anything we can observe
*), which is applied to a quantum state. It's corresponding so-called eigenvalues are what we measure as energy, which are quantisized. This means that they can only appear as products with integers. (e.g, you could have an energy of 123.3 Mev and 154.13 MeV but not anything in between). An interesting consequence of this is that a quantum system has a minimum non-zero
energy. So strings have some 'vacuum state'. (EDIT: Not to be confused with the ground state, which is the minimum energy in typical quantum mechanics). They can also gain and lose energy through various interactions. These interactions are governed by the laws of quantum field theory.
*A very important concept in quantum physics
I don't think I understand the question. Vibration is not a physical quantity, by itself. We could define frequency, for instance. But not compare it to speed. If your question really means "does the speed of light 'barrier' apply to strings", then the answer is yes.