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#:The cited article never mentions relativity or the possibility that relativity is wrong.  In fact, the entire discussion is in the context of black holes.  The second study was about a black hole at the center of a galaxy apparently wandering out of place.  The hypothesis is that a merger of two galaxies was involved, and "the theoretical prediction is that when two black holes merge, the newly combined black hole receives a 'kick' due to the emission of gravitational waves ..."  Gravitational waves are, of course, a specific prediction of general relativity.

#:The cited article never mentions relativity or the possibility that relativity is wrong.  In fact, the entire discussion is in the context of black holes.  The second study was about a black hole at the center of a galaxy apparently wandering out of place.  The hypothesis is that a merger of two galaxies was involved, and "the theoretical prediction is that when two black holes merge, the newly combined black hole receives a 'kick' due to the emission of gravitational waves ..."  Gravitational waves are, of course, a specific prediction of general relativity.

#''Apparently, the equations of General Relativity do not apply to the motions of extra-solar planets.''

#''Apparently, the equations of General Relativity do not apply to the motions of extra-solar planets.''

#:This refers to a recently discovered planetary system in which another star is closer than had previously been seen in such a system.  Systems involving two stars and a planet constitute the "three body problem", which has never been solved analytically.  But if only one of the objects is massive, such as the Sun, the system can be stable for all practical purposes, which is why the solar system is effectively stable even though it is a many-body problem.  But two stars make the system much more problematical.  In the past, such systems have had the other star far enough away that it has essentially no effect.  The Gamma Cephei system is different, and scientists are eager to analyze it in detail.  They are frustrated in this by the extremely scant data about the planet's orbit, since that information has to be gleaned from tiny spectroscopic shifts (in only one dimension!) of the two stars.

#:This refers to a recently discovered planetary system in which another star is closer than had previously been seen in such a system.  Systems involving two stars and a planet constitute the "three body problem", which has never been solved analytically.  But if only one of the objects is massive, such as the Sun, the system can be stable for all practical purposes, which is why the solar system is effectively stable even though it is a many-body problem.  But two stars make the system much more problematical.  In the past, such systems have had the other star far enough away that it has essentially no effect.  The Gamma Cephei system is different, and scientists are eager to analyze it in detail.  They are frustrated in this by the extremely scant data about the planet's orbit, since that information has to be gleaned from tiny spectroscopic shifts (in only one dimension!) of the two stars.