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When you attach an Individual Character to a unit of elites does it all count as one unit with the same point costs or does it count as two separate units. If the latter, what is the advantage of attaching units?

It counts as two seperate units, the IC and the squad.

The advantage is that if the unit is shot at, you can allocate wounds to the squad, therefore saving the IC, or the other way around, using an IC's save to protect a valuable unit.
(The first option is more sensible, as IC's are often points heavy and not suitable for meat sheild duties.)

It is one unit (page 48 and page 49) that, in combat, is two units for the purpose of resolving attacks.

By attaching an IC to another unit you cannot shoot directly at the IC any longer; without this protection your average marine IC (T4, no Eternal Warrior) wouldnt last long against lascannons...