I must admit I know very, very little about timelike quantum entanglement, as it is a very new field of research. I do not know of how anyone could create timelike entangled particles, and I'm unsure if anyone has any ideas at this very early stage.

As far as what implications this may have, it could very well give us new insight into the nature of spacetime. Because relativity tells us that time and space are intimately connected, the existence of spacelike entangled particles (which are known to exist, and many experiments have been done on them) implies that timelike entangled particles should exist. Entanglement is a property of quantum mechanics, which currently is not fully compatible with general relativity. Timelike entangled particles could provide a new means of probing how to reconcile quantum mechanics with general relativity.

It could additionally provide a tool for emerging technologies such as quantum computation and quantum cryptography. However, it must be emphasized that even though there is an entanglement of particles spanning a length of time, it is unlikely we would ever be able to 'teleport' information into the future in any meaningful way that breaks the speed-of-light speed limit in the universe. And based on our current understanding of the reality of the universe, information transmission into the past is likely to always remain a topic for science fiction.

The idea as I understand it is that information cannot travel at a speed greater than that of light, but when you emit a stream of electrons through a magnetic field, one of the beams of them will be spin up and the other will be spin down. However, the wave function of the electrons' spin is collapsed when you measure it, and by collapsing the wave function on one beam, you instantly collapse it on the other beam. I do not understand quantum mechanics or relativity to explain to you why this is a challenge to our understanding of physics, or how it was solved. You really do need to talk to your physics professor (or TA) at your university.