No. While gradient elution is common in reversed phase HPLC for many applications isocratic is viable. Probably the majority of reverse phase separations are performed under isocratic conditions. Gradients are generally only employed in order to solve the general elution problem (i.e. the mobile phase necessary for retention of an early eluting peak results in infinite K'for a late eluting peak). There are other benefits of performing a gradient such as improved sensitivity since peaks are narrower under gradient conditions but generally this isn't the primary reason that one employees gradient elution.
It is the molecule and its solubility in reverse or normal phase solvents that determine which mode you use. Gradient is used to separate related substances that are chemically and structurally similar to the molecule of interest. Isocratic is commonly used,when the separation criteria is not intense.
Not really, since it's all historical. Normal phase was initially used back in the 1970's since it was developed(?) from gas chromatography. The HPLC column was just silica and Hexane (a non-polar solvent) was used. But most molecules are polar and soluble in solvents that have a low UV cutoff (like Water, Methanol, Acetonitrile, IPA). Thus the UV detector and development of the PDA/DAD. In addition column technology advanced and made HPLC columns more non-polar by adding silanol groups (thus C18 or ODS). This is the birth of 'reverse phase chromatography' since these molecules elute in reverse order' from normal. The column story continues by endcapping columns using proprietary manufacturing processes. Stay tuned!
Both, reverse phase (RPC) and normal phase chromatography, are suitable to be used in isocratic and also gradient conditions. For example, on the other hand, gel permeation cromatography (GPC) can be used only in isocratic conditions.
Reversed-phase chromatography refers to all chromatographic methods which use a hydrophobic stationary phase (into the column).
Reverse Phase and Normal Phase Chromatography can be used either in Isocratic mode or Gradient mode. The selection of the mode depends largely on the sample type. Generally for complex samples, we prefer gradient mode like in GC we do temperature programming. The change in polarity of the mobile phase during the run helps in better separation and peak shape. In Reverse Phase, the column is non-polar and the mobile phase is polar. In Normal Phase, the column is polar (e.g. Si column) and the mobile phase is non-polar. In gradient elution also, you have different options like linear gradient, concave, convex etc to suit your sample type.