Does the Genesis machine make sense?

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The genesis device itself is from a place where there is no sun.

Since you're eager for a response, I'll try my best:

The Genesis Project, as shown in action in that video, is basically what the Genesis Device does: terraform a planet-sized rocky body, nothing more.

I honestly don't think that Genesis can create suns: I can only guess that the test site had a massive artificial light source, nothing more, and it was NOT created by Genesis. As for the full-size planet at the end, I can guess that even though a planet was created out of the matter of the nebula, it was not intended to be used this way, needed a rocky body to work properly, and used Protomatter anyway, which was unstable enough, especially on a nebula. The sun for the newly-formed world must've been already there, a local nearby star which just happened to be near the detonation of Genesis.

Considering how massive suns are relative to their orbiting planets (and our sun is massive compared to Earth, and our sun is TINY compared to some stars), not to mention their extremely volatile nature (massive amounts of nuclear fusion energy contained by massive gravity), I seriously don't think that Federation scientists can go so far as to create them, and never could. They can blow them up easily (trilithium) but that's another story.

There is another factor: IF the sun had been created by Genesis, it would've exploded in a supernova around the same time that the planet itself disintegrated, and our heroes would be dead. It didn't, so we can assume that the sun was not created by Genesis.

No, Genesis does not create suns, only what the video said. Otherwise, a sun would've been featured, too.

It never made any sense to me how Kirk and company were eating apples from the Genesis cave, and then later on, the Genesis planet was revealed to be unstable and began to destroy itself. Wouldn't those apples grown in the Genesis cave cause some serious damage to anyone who ate them?

another factor/reason why the Genesis planet was unstable was because Kirk and gang and Khan were all in the Mutara Nebula .

I haven't seen this in a while, but I don't remember Genesis creating a sun.