Half-elves get a trait called "multitalented." The rules describe it briefly: Half-elves choose two favored classes at first level and gain +1 hit point or +1 skill point whenever they take a level in either one of those classes.
Does this mean that (aside from the obvious two favored classes) half-elves can multiclass at first level?
Nothing in the race's description[PFSRD] nor in the multiclassing rules[PFSRD] mentions any exceptions for half elves. Especially the multiclassing rules seem to explicitly exclude the option of multiclassing at character level 1:
Instead of gaining the abilities granted by the next level in your character's current class, he can instead gain the 1st-level abilities of a new class, adding all of those abilities to his existing ones. This is known as “multiclassing.” [...]
This strongly indicates that half elves start with a single character class like all other characters.
My guess is that this racial trait should encourage builds including multiple base classes - like e.g. monk/rogue or fighter/wizard - to showcase the half elves' natural adaptability and flexibility.
A half elf character multiclassing between his two favored classes gets more out of it than a human or elf character with the same class combination.
Every level your character gains you can gain a level in a single class. Multi classing is when you split these class levels across multiple classes. For example when your character (let's say a gnome Wizard) reaches 5th level you decides to multi-class into a cleric. Your character is level 5, but more specifically a level 4 Wizard and a level 1 Cleric. (note: multi-classing is a little more involved than this, but this is the relevant part to your question)
Picking a favored class grants you an additional hit point or skill point for every level you take of that class. So if your gnome had wizard as its favored class, it would gain an additional hit or skill point for each of the first 4 levels, but not when it hit level 5 and took a level of Cleric.
Half-elves still level the same as every other class, but have multi-talented, which allows them to pick two favored classes. If our gnomish example character was a Half-elf, we would want to keep our favored class as wizard, but also make Cleric a favored class. Now when the character reached 5th level and took a level in Cleric, they would still gain an additional hit or skill point.
No. There's another question that has an in depth example of how favored classes and racial benefits work for half-elves you may want to peruse: How do favored classes work in Pathfinder?
