Is it explained anything about what turned the cellphone-microphone into a time machine? (not how it is operated) So they created a time machine with a microwave and a cellphone. As far as I've seen in the anime series, something it is explained about how to operate it, but do the characters ever explain something about what makes it work? Do they give any Physics related explanation about what made the microwave and cellphone capable of sending things into the past?
I think the original visual novel goes into more detail on this.  Basically, time travel in Steins;Gate universe requires the use of a black hole. Sern is able to create them (though very tiny ones) using their large hadron collider (this was theorized as possible in real life with CERN's LHC, though I'm not sure if that theory was ever proven or disproven.)

So basically, the explanation for the phone microwave was that by lucky accident, they created their own particle collider. Remember one of the key components of their phone microwave was the large CRT television in the downstairs shop, which they referred to as the "lifter" as in ion-propelled aircraft. Cathode ray tube televisions function by shooting a beam of electrons at the screen, and thus they handwaved it to be the same as the beams of particles used in the LHC (obviously it's not). Also, as to how this combined with the microwave to create mini Kerr blackholes was as I recall unclear. 

The time-leap machine was not a separate machine, but an addition to the phone microwave, that converted memories into data that was sent instead of a normal SMS. This was even more handwave-y because there's no way all a person's memories could be contained in the small number of bytes being sent by the phone microwave. They excused it by the blackhole physically "compressing" the data, as I recall, which is a very fundamental misunderstanding of how data compression even works. The black hole's "compression" effect was also what was turning matter that went into the black hole into green goo. 

Anyways, that's my recollection, since I was unable to find very good resources on it, and I'm not about to replay the visual novel right now to jog the memory.