[RPG] How to a Cleric gain extra uses of a domain ability

If you choose the Arcane bloodline then no, there are no bloodline powers that the Halfling favoured class option can apply to. But this doesn't mean that you don't gain any bonuses for sorcerer being your favoured class, you just fall back to the standard options. You can only chose the +1 hit point or skill rank per level.

If you wanted to use the Halfling's favoured class option then you would have to choose a different blood line, one with a power that meets the requirements, such as Celestial (Heavenly Fire power).

You can, but it won't help you in these cases.

The target is a creature, which definitely includes you unless you are an inanimate object.

The effects will likely not help you, since

Effects that last a certain number of rounds end just before the same initiative count that they began on.

(Core Rulebook page 178). So it usually only helps yourself with attacks of opportunity.