A quick word: You want "science-based". I think what I gave you fits this according to what I encounter elsewhere on worldbuilding. I have to say in my defense though: We are dealing with very advanced aliens. What they might be able to build could seem impossible for us. So I'm not going to give you any design specifications. If you want blueprints for your ship and what (magnetic?) field strength is required, I think you should add that to your answer. This answer is sci fi and not sci. I hope it still is acceptable to you.
What you are looking for is called a "fusion reactor". Stars are just objects large (heavy, dense, ...) enough to sustain hydrogen fusion without any help. A fusion reactor is the artificial version of that. Since they do exist more or less, I do not think I need to give you blueprints, you can google that. I'm here to persuade you to consider an artificial star. A space ship could very well be powered by a hydrogen fusion reactor. There are several advantages to having your spaceship being powered by such an reactor over a natural star:
1) The fusion reactor will produce the amount of energy needed for the ship, not too much and not too little.
2) You can build as many fusion reactors as you want. There are pretty few stars around locally, for example our solar system only has 1 and we need that one.
3) You will not face the same problems with radiation, unpredictable outbursts and so on. I'm not saying that wouldn't be a problem in a very big implementation of a fusion reactor, but at least I'd buy that super advanced aliens found a way to reduce unwanted radiation.
4) It is pretty easy to drag a fusion reactor along and integrate into your ship. A star is pretty massive and once you have accelerated, the more mass you have the more inertia you have to deal with. Remember, a small star burns for billions of years. That is a lot of extra fuel you do not need.
5) Stars are pretty big. I'm not sure you are aware of that. All you would see at the end is a star flying through space and not a spaceship with a star in it's tow, but I might picture your design the wrong way. That would be some ship otherwise ... In any case, a star is super bright. Even if you have such a large ship, one might not even be able to see it. Ever tried looking directly at the sun? (don't do it)
6) You have limitations on how big your spaceship can be if you take natural occurring stars. A fusion reactor can have any size you want.
I'm sure there is a lot more.
There are no drawbacks I'm aware of. You might think: But I want a bright light and a huge ship? Well, just make the fusion reactor really big. As big as you want. Make it emit light, maybe not as bright as a star so that people can still see it in its magnificent beauty. But I don't think a spaceship with a real star inside is something anyone would seriously consider doing.
What a fusion reactor is and what isn't is maybe a bit of a debatable topic. One could end up at "artificial stars" (I don't think so though, see my "extra fuel" point), but if you ask me they are still fusion reactors, designed as you please to fit your needs. To the people that encounter your spaceship, it very well might look like they caught a star.
As for your force field, read this for example. Combine it with the Alien technology you just made up. Yes, I know it wouldn't hold on such a big scale, we actually have problems if we want that thing earth-sized. You can just say the Aliens found a way. If you want other ideas (I would go with several reactors that from a distance look like one big star), well, I do not want to write even more stuff if you end up hating the idea.