Andres,
I'm not sure exactly when it happened, but at some time in the past ABYC changed the rules, and began requiring GFCI outlets in boats. Catalina obeyed the rules, and installed them in our boats. Rather than making each outlet a GFCI outlet, they made the first one in a series a GFCI, and then wired the rest of the outlets "dowstream" of the GFCI. This way the downstream outlets are protected, too. You may have tripped the GFCI outlet, which would cause them to have no power. Inspect each of your outlets carefully. One of them (possibly two of them?) is most likely a GFCI outlet with the tiny TEST and RESET buttons in it. Press the RESET button, and you should be good to go. If this is not the case, then you need to grab a multi-meter and do some investigating. If you do not feel comfortable doing this, hire a qualified electrician for a hour, and follow him around the boat, taking notes. It will be well worth the minor expense. Hope this helps.

First question I'd ask you is this; do you feel comfortable working on your electrical system at home? If not, you're probably better off getting someone who's qualified to work on the shore power system on your boat. Just for safety.

To address your questions:
1 - yes the battery switch needs to be on if you want to use any of the 12 volt components, eg;, lights, fresh water pump, etc.
2 - see above
3 - my boat is a '97 with all of the original breakers. Unless they're bad, I'd see no reason to replace them.
4 - I believe all of the 110 volt breakers are 20 amp, but they should have a label on them.
5 - first thing to check is that the breaker for the outlets is pushed in. If it's out, they have either been turned off by pressing the button, or the breaker has tripped. If it's tripped, you need to find out why.
second thing to check; the first outlet on each side of the boat is a GFCI. If the button on the outlet is tripped, all outlets downstream will be off as well. There is a test and reset button on these outlets. On my boat, one is at the nav station, the other is on the bulkhead near the aft corner of the galley, above the fridge.

Hope that helps. I'd vote for the GFCI being tripped, that happens occasionally on my boat, usually when I'm not there.

In the past I would have the same problem when I first plugged in the shore power after a day sail. I found that it was because the house batteries were depleted and the battery charger was taking more current than the shore power was able to handle. That was because I was too lazy to switch to "ALL" before I turned on the engine to charge all the batteries while engining into the doc. Now I place the battery to ALL, then turn on the engine. I have not had that problem since.

Andres,
As Gary stated above, the battery switch needs to be on if you want to use any 12V things. The shore power cord brings 110V power into the boat (I assume it IS 110V, and not 220V???), and from there gets distributed to the battery charger, water heater, and outlets, all through breakers. The 110V AC system and the 12V DC systems are not connected to each other, except through the batter charger (you use 110V AC to charge your 12V DC batteries). As to whether the battery switch should be set to 1 or 2 or BOTH depends on how your battery charger is wired. If your battery charger has two outputs, and they are each wired to your batteries directly, or if you have an echo charger, then the battery switch has no bearing on what's being charged. If, on the other hand, your battery charger has one output, and is wired to one battery (doubtful), then you need to switch to BOTH to charge your batteries. You probably can't go wrong switching to BOTH when charging the batteries from shore power. Also as Gary mentioned, check the breakers for the 110V items (water heater, battery charger, and outlets). The circuitry is very simple, but 110V can kill you, so ask a professional if you are not sure.

Andres-
When I hook up shore power- I make sure all circuits are turned off on the boat. My boat has an AC breaker/surge protector in the aft starboard locker. This receives the power from the shore connection and I have to throw the switch in the locker to get current to the rest of the boat including the polarity indicator light. After activating that switch, I activate my main DC breaker- a throw switch located in the starboard settee. Then, I turn my battery selector switch to the on position for the house batteries. Lastly, I activate any of the individual DC circuit switches I need- like the one for the battery charger etc. I go through the reverse procedure to remove AC power. However, I believe boats have various set ups and I'm not sure if the original owner added some features to mine (Like the circuit breakers adjacent the shore power receptacle). I have several outlets with GFI . I too suspect a GFI is tripped if you are not getting power to the outlets. By the way- I have two shore power inlets- one is dedicated to my AC/Heatpump and does not power the outlets, refrigeration or charger. I mention that in the event you have two.

Possibly if you have an inverter/charger, make sure inverter is on