My CV fleets were sunk by mixed fleets or SAG's. That means
a) Yes, of course you "can touch this". I am not sure where this misconception comes from because I see it happen in every single game.
b) CV's in "close combat" are not very effective. I imagine that if I had had some BB's of my own, they would either have drawn some fire or incurred some losses themselves.
c) Escorts die likes flies. At times, one side or both will have lost 3+ escorts when the screen pops up, ie. in the opening salvo.
Positioning is critical for any battle.
A great example for this is the
Battle of Samar. But I will come back to that game mechanic later in my posting.
First, about your statements:
(a) Yes you can, but a pure CV fleet under a good commander will usually start out of range. It can happen, but if your fleet setup is good, it won't happen too often.
(b) CVs are useless in close quarter combat, but, well, that's as it is. But remember that CAGs from CVs are always in perfect combat position no matter at what range your CVs start. Adding BB to a carrier fleet does not help. It worsens your positioning, making it more likely for your CVs to start at point blank range. On the other hand, a regular melee fleet will overcome your addtional BBs easily, so at best you will sacrifice some Battleships to get your CVs out of close combat (that was caused because you added BB in the first place). Which brings us to:
(c) Yes, they do. Escorts are fragile and easy to destroy and during a large battle, your escorts will be the first ships to go to the bottom of the sea. But, believe it or not: That is actually a good thing. Your escorts draw fire from your enemy and give your other units time to make their attack. In regards to your comment (b), that means it is actually more feasible to add a larger escort of DDs to your CVs intead of adding BBs. You can probably get around 6 DDs for the same hullsize of a single battleship - and while these 6 DDs might have less combined firepower, they will make the enemy spread his attacks and give your CVs the time to run they need. With some luck, you can disengage from combat fast enough and end up with a pack of (heavily) damaged DDs instead of several sunken capital ships. Oh and of course a large number of small ships provides better protection (more targets) and offensive firepower against enemy air attacks.
So always have several DD flottillas ready to replace your regular escorts. In general, I try to have twice the amount of active escorts as a reserve force on standby.
Positioning is critical for any battle.
I learned it the hard way when I was playing the US. I had a mixed fleet with 5 CV, 3 BB and 10 CL escorts - and was completly annihilated by a japanese fleet consisting of 4 BB, 2 BC, 4 CA and around a total of 20 DD and CL escorts.
The Japanese had taken my fleet by surprise, at least all my CVs started in firing range of the enemy - and before they were able to withdraw, Lexington and Enterprise had already sunk, while the three others suffered heavy damage. My BBs were overwhelmed quickly and sunk after 8 hours of combat, while most of my escorting DD spread their fire, causing little damage on the enemy. In the end I had lost all but 1 CV that managed to make it back to Guam.
I think I could have avoided that desaster if I had used smaller DD instead of CL and if I would have made a "pure" CV fleet instead of adding BB.
Keep your total hull size as small as possible while aquiring as much firepower as possible. If you exceed your hullsize limit, your forces will not only receive a combat penalty, but will also suffer from reduced positioning. You can still get lucky - like the Japanese did in the above example - but luck is no reliable combat factor.
In the end, HoI3 naval combat comes down to mass strike tactics. And while hull size penalties eliminate the classic BB, BC, CL or DD Zerg from HoI2, it does not prevent Carrier doomstacks. Remember that CAG on CAG duty (that includes their auto-attack during naval combat) suffer a smaller stacking penalty, hence you can stack over 30 CAG squads into a single battle without any real consquences.
Once you meet a fleet consisting of 12 CV and 12 DD on the open sea, you will understand what "overkill" really means. Against 24 active CAGs, your ships will sink faster than you can say "turkey shoot". And considering the enormous firepower of this fleet, it's hull size penalty is actually rather low. You could never ever achieve that with any other combination of ships...