According to the rules: In the event that a class feature or other special ability provides an adjustment to your caster level, that adjustment applies not only to effects based on caster level (such as range, duration, and damage dealt), but also to your caster level check to overcome your target's spell resistance and to the caster level used in dispel checks (both the dispel check and the DC of the check).
What about BAB? For example, spells like spiritual weapon rely on the BAB of the caster. Does that mean that if a feat/trait let me cast the spell at CL+1, the effect (to hit) is also based on BAB of the next cleric level?
No.
The effect is what happens if you hit.