Sorry, but the deductions you make here from the famous "E = M*C^2" are wrong.
The formula just states that energy is equivalent to mass, C (or C^2) just happens to be a scaling factor (like *10), but this formula does NOT take into account at what speed the mass M is moving, so it doesn't allow any conclusion about "mass increases with speed". The latter is true, but it cannot be derived from this particular formula.
And in general, "faster than light" is nothing new, i.e. see the following:
- Cherenkov radiation (matter moving faster than light travels through water, C[water] is 75% of C[vacuum]...)
- Tunnel effect, where particle "tunnel" through mass and leave the mass even before they enter it: speed>C
- Quantum entanglement where two entangled subatomic particles change certain properties at the same time, no matter the distance, hinting they are connected in a way that makes them at least exchange information faster than light (instantly).
- And last but not least tachyons - their existance still needs to be proven though, but they are nowhere near "new".
/Edit:
And neutrinos hardly interact with mass, so detecting them is very complicated already, let alone statements about their exact speed...