No, there's only Spheres of Might, no Spheres of Power.
RSF is always based on base class not on any archetype. So the 1/2 progression spellcasting grants 20RSF, even if you choose NOT to buy it back at 4th level. this is the same amount for any "System" progression, ie magic, Psionics, Spheres of Might, Manuevers. So yes, partial progression classes get a big boost.
I don't think you could make a Paladin a full caster, because there isn't an archetype to do it, Not sure there's ways to change the progression speed outside of Spheres. One of the answers implies that you can always buy SoM progression even if your class doesn't normally get it but I'd like a clarification from DM on that