Is it possible for a star to orbit a planet IF the planet is bigger than the said star? Or is it possible even if the star is bigger than the planet and still the star is orbiting the planet? I have done some research with no results.
Technically stars and planets orbit a common barycenter. In case of single star systems the barycenter is usually within the star. However, the barycenter between the Sun and Jupiter is outside the Sun (though very close to it). Otherwise, colloquially, when we say something orbits another body, the body that's "being orbited" is usually the most massive one. Since stars are more massive than planets, it's the planets that orbit them.
A gas giant needs more than 12.5 Jupiter masses to start deuterium fusion, thus becoming a brown dwarf star. That doesn't mean it will. From about 15 Jovian masses on I guess it definitely will, so there's a grey zone between 12.5 and 15 Jovian masses where a more massive gas giant might not fuse deuterium (therefore being a sub-brown dwarf planet) and a less massive could (thus being a brown dwarf star). This is the only case where you might say a star orbits a planet though in fact they'd orbit a barycenter that would be outside either body.
And since black holes count as stars, you may want to consider primordial black holes stars which are less massive than gas giant planets, so if they orbit a gas giant that would be another case of a star orbiting a planet. But we're unsure whether such PBHs exist.
There might also be planets close enough to a stellar black hole that are big enough so that the barycenter is closer to the planet but I'm unsure whether the black hole's tidal forces wouldn't tear the planet apart in such case.