The star is usually not assumed to be a perfect sphere ... the shape of stars is determined by physics that are well known.
Most stars would be oblate due to their rotation ... but only slightly so a sphere is a very good approximation - especially considering the distances involved.
We can be sure of this for distant stars the same way we can be sure of anything - we check for nearby stars, and assume that the laws of physics are pretty much the same everywhere.
However the shape of the star is not important for detecting bodies orbiting it.
Pulsations of stars are indeed something that can mess up radial velocity and intensity measurements, but those pulsations don't have the same structure as influences of planets, so it is possible to separate them. In the worst case you just stop looking for planets around a star that is too chaotic.