Quantum Tunneling and Negative Kinetic energy

The questions you asked belongs to two distinctly different way of thinking. Tunneling effect is quite easy and I would ask you to consult any standard book eg Zettlii. I would love to explain the second phenomenon with negative energy situation which can be explained using quantum field theory or more precisely with proper knowledge of Dirac equation. Let us not discuss any mathematical derivations here cause you can consult any standard book of relativistic Quantum Mechanics for Dirac equation, here we will have to discuss Dirac's Hole Theory. Negative energy of free particle was a great problem for stability of a system as it forces systems to collapse. Dirac at showed that his theory is basically consistent with spin half particles and as they obey Pauli's exclusion principle not all the particles can obtain the lowest energy state and in this way a system of Fermions gets stable. But here is a big question, where is those particles with negative energies? Dirac said that these particles basically don't "shows" their existence. They don't show any property like mass or charge and they don't even react with other systems. But if we can bomber one particle with a photon of sufficient energy then we can displace one such particle but the vacant place isn't "vacuum" rather it's a "hole" (please don't think it as you heard in electronics or solid state) with equal mass but opposite charge. This is actually the antiparticle of the particle.

I hope you get a clear glimpse of what I'm trying to say, it's a vast thing and if you're interested for further study I'll ask you to consult first two chapters of quantum field theory book by Ashok Dass.

I hope it was helpful, thank you.