I don't want to do the same thing twice. For example: i don't see the difference between a barbell-curl and dumbell curls.
There is a difference between barbell and dumbell curls. Like supremefresh said, dumbell curls force each arm to lift it's own weight. Barbell curls are the cornerstone of a bicep workout, since they allow you to lift the most amount of weight. Even though these two exercises are different in this way, the bottom line is you're still working out the biceps, and because of the function that muscle, or any muscle really, you are limited to a certain number of exercises you can do. Three different exercises per muscle group is great, but keep in mind that those exercises are going to be somewhat similar to each other no matter what.
Moving on to the inner/outer head thing- I've heard that a wider grip is supposed to work out the inner head of the biceps and a closer grip is good for the outer head- as for the triceps, if you do tricep pressdowns, lying tricep extensions and dumbell kickbacks, that should cover the various angles you can hit the tri's from.
On another note, why only the arms? What about the rest of your body? If you're not working everything else with the same intensity you're interested in for your arms, your arms will not get that big- You cannot curl real heavy weights if your lower back is proportionally weaker, for example. You never see anyone with twenty inch biceps and tiny shoulders either- If you only work out your arms, you'll hit a plateau and not be able to lift any more.
Of course, I don't know what the rest of your workout looks like- I don't want to be putting my foot in my mouth if you already have a workout schedule that does include everything.