As per the description of Spellsword:
Spellswords gain one caster level every other level after the first (respectively at 1,3,5,7,9) gaining all benefits of durations and improved spellcasting, but not any other benefits from their spellcasting class.
Does that mean that when you gain a caster level it increases the number of spell slots and opens up spell slots in the corresponding spell level? If so, can a Spellsword acquire scrolls to add into their spell book for use in the spell levels that they gain access to through the Spellsword levels?