I haven't seen where to switch commanders, but I will look into it with my next scenario (tonight).
When you create a TF, after you exit the ship selection screen, you can click on the icon for your just-created TF near the bottome of the screen. This brings up the TF info screen. On the left hand side, you'll see the name of the TF commander in yellow text. If you click on that, you can select a new commander.
If I can see them, logically so can the commander on the carriers, right? If, for example, a long range search plane from RAbaul spots a US carrier and it is reported to me (via an icon on my screen), this report would be transmitted to the relevant commanders in the theater? Or does a search plane from the carrier need to spot the contact for that commander to know about it?
Yes, if a search plane spotted a TF, then every local AI commander knows about it. Whether or not they actually decide to do something about it, is another matter. There are many little things that can prevent effective use of air assets at a base, that can be found in the manual. One of these is that if the number of planes at a given base exceeds the amount of air support, then performance of the whole base is degraded. Base force units supply needed air support. On the base screen, you'll see an entry for "Air Support" and "Air Support Needed". If either of these two entries is in red text, then you need to send another air support unit to that base.
Also, if the number of planes at the airbase exceeds 50x the size of the airfield, then effectiveness suffers considerably. For example, if the airbase is size 4, then it can comfortably handle 200 aircraft without penalty(4x50=200). But if you have 250 aircraft stuffed into that base, then obviously the groundcrew can't cope with that many, so fewer flights will be ordered.
Another thing to be careful about is weather. Ordering flight ops on days that are filled with thunderstorms, will wear your pilots out, and cause uneccessary operational losses. Not to mention that the escort may not be able to find the bombers to escort, the bombers may get lost and rtb without attacking, etc.
Keep your pilots well-rested, and when their fatigue is over 25, give them a break for a day or two. When a huge battle is imminent, of course, then you will have to fly them no matter what their fatigue. But woe be to the commander who pushes his men too hard.