Your Level, when in a class description is your Class Level; in almost all other places, it's your Character Level.
Character Level is the sum of all your Class levels, plus any racial adjustment if importing D20 races with Level adjustments. (IIRC, Pathfinder doesn't use level adjustments; all they are is a class that can't be raised.)
Class Level is the number of times you've increased that particular class, including the one level you start the game with. It only affects that particular class, normally
Caster Level is the total class levels of all classes using the same type of magic.
Example: A Wizard 3/Fighter 4 has a Wizard Class Level of 3, a fighter Class Level of 4, and a Character Level of 7, and is an Arcane Caster Level 3.
Example: A Wizard 9/Spellsinger 2/Rogue 2 is Wizard Class Level 9, Spellsinger Class Level 2, and Rogue class level 2. Her Arcane Caster Level is 11, because Spellsinger adds to her arcane caster level... she casts as an 11th level wizard, but only has 9th level class features from wizard; her two levels of Spellsinger class levels giver her the 2nd level class features. Her Character Level is 13
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).
Best Answer
Under section 4 of the Character Creation Outline it states "...and the choice of gaining a hit point or a skill rank each time a character gains a level (including his first level)..."
So, yes, the favored class bonus does apply at 1st level.