The language that you are using makes it very difficult to answer your questions.  A qualifying child must live with you for over half the year, but they do not have a gross income test - they just cannot provide over half of their own support.  A qualifying relative, either does not have to live you with you at all, or if not actually a relative, must live with you for all 12 months.  A qualifying relative cannot have a gross income more than $4,150 in 2018.

The limit that you posted is a tortured version of the standard deduction for dependents which is the higher of earned income + 350 or $1,050, but does not have anything to do with the gross income test for a qualifying relative.