This is a tuffy, Let's ditch most of the science and hit specific problems.
It can't eat in the normal way. There is just nothing to eat. Photosynthesis gives us a decent model, but stars are really far a part, a space turnip isn't going to make it much further from the sun then earth is. So let's look at what is more "available" then light. Gamma Radiation, X-Ray Radiation, and the like. So basically "Radiation" is a food source. It could work, but it wouldn't give very much energy.
It defecates I don't see this happening. It would have to "use" almost 100% of the energy that it collects. See the section on thrusters though.
It moves Well, ok, so long as it doesn't move much, sure why not. If it moves too much you have an energy problem again. I would say it would be ok to "spasm" every once in a long while.
It grows Sure, why not. The problem is growing takes more energy then maintaining. With such a rare food intake, that precious energy probably can't go too much to growing.
It ejects eggs, attracts mates, and has sex in interstellar space Unless your writing space whale porn, let this one go. For all known lifeforms, sexual reproduction is a energy intensive task. Even plants, and they let someone else do all the work. Super abstract, all the energy of making an egg and a sperm, then finding a mate, sharing it, and hatching it, that's quite a bit of waste. Have them produce a-sexually. It's "easier". Once they reach a certain size, they split. In this case the "mother" split would need to die in 90% of the cases. Only if it was really lucky would the mother bit get to live.
It has skin that pressurizes its insides so that its insides are pressurized even when the organism lives in the vacuum of space. Why, There is no need for this. In this odd lifeforms, it's insides don't need air-pressure. It can evolve ways around that.
It has thrusters on its back that it can eject fuel out of to change its velocity. This is another odd one. I think you might be better off with "farts to change direction" There is not a lot in space, so where are you going to get this fuel. Assuming that this thing eats "radiation" it's gonna need a lot of it. You can get some propulsion by "emitting radiation" but not as much as your going to need. Look to satellites' magnetic engines for your best, currently known bet, and do something like that.
It is capable of accelerating to 50% the speed of light relative to the rest of the galaxy in 3 months allowing it to cover astronomical distances in search of food and mates. First, that's horribly slow. That's 8 years between star systems. The good news is, that as long as you don't care about slowing down, I suppose it's doable. It can speed up really really slowly, absorbing the radiation of a star as it gets closer, smashing into it, destroying it, and absorbing some matter in the process. Then fart propel it's self in a minor coarse correction, leaving behind a decimated ruin or a solar system.
Its eyesight is so good that it can see an object the size of Saturn from as far as Earth as a human seeing a baseball at a distance of 0.1m. Yeah, that's pretty crappy on interstellar terms. Using the normal analogy of Sol to Alpha century when both are the size of grapefruit, you would need to see that grapefruit from across the US. The good news is that because it eats "radiation" it doesn't have to "see" just has to point it's self at the most tasty radiation it can. And because it only has minor fart propulsion, it's not going to get a bunch of choices.
It has bioluminescence that allows it to be seen by potential mates. Unless it can light up brighter then a star, no it doesn't. It simply won't work. You can make it shiny though as a side effect of absorbing the "radiation".
What your left with:
You would have a MASSIVE lifeform, that basically, breaks wind in a single direction, hoping to find enough "Radiation" to sustain it's self. It wouldn't be very smart, it doesn't have the energy for that. Every 200 billion years or so it would clone it's self, without slowing down mind you, let out a massive fart (of radiation) and change direction by 0.0000001 degrees.
The creature would need to live near forever, it would be HUGE and would wipe out any solar system it came near.
I would not want to run into one of these.