Can I eat at a kosher restaurant that opens on Shabbos?

Listen, this is an important question, and the answer depends on a few factors. If you're talking about eating at a specific branch of a chain restaurant that is closed on Shabbos, even though other branches of the same chain open on Shabbos, technically there is no issur to eat at that specific branch that remains closed. However, it's certainly preferable to support businesses that are completely shomrei Shabbos. Now, if the restaurant itself is open on Shabbos, you have a serious problem. Why? Because if the owner doesn't keep Shabbos, he cannot be trusted. If he doesn't care enough about his own neshama to keep Shabbos, why would he care about your neshama to ensure the food is truly kosher? This is a fundamental principle. In Eretz Yisrael, the Rabbanut will not give a kosher certificate to any restaurant whose owner is mechalel Shabbos, even if the meat itself is kosher. The reason is simple: someone who violates Shabbos shows he doesn't care about Torah, and therefore cannot be relied upon. Even if there's a mashgiach present and the ingredients are kosher, if the owner himself is mechalel Shabbos, there are too many opportunities for problems. He could bring in non-kosher products, use utensils improperly, or cut corners when nobody is watching. The only exception might be if there's a reliable mashgiach who turns on the fire and oversees everything constantly, treating the non-shomer-Shabbos owner like a goy. But even then, it's far from ideal. The bottom line is this: you should only eat at restaurants owned by religious people who keep Shabbos. Don't give your business to someone who is openly violating the Torah. There are plenty of kosher options available today, baruch Hashem. Find a place with a good hechsher and an owner who is shomer Shabbos. That's what you should do.