But (this is my doubt) in this configuration is necessary a capacitor (VCC to GND) near the signal via, in order to provide an adjacent return path for the current.
Yes. For stackup A, you will want a nearby decoupling capacitor wherever your signals transition between Signal1 and Signal2 or between Signal3 and Signal4.
Not only do these capacitors take up space and cost money, but also, they force your return current to take a longer path than it would have to if it could just transition from one side of a copper plane to the other, so they introduce some EMI risk.
[With stackup B] I have only one buried capacitor
I wouldn't worry too much about trying to make buried capacitance. Answering a recent question I worked out roughly the value of capacitance you can build in to a board. You have a multilayer board, so you can have much smaller plane-plane distance than the guy who asked that question, but you also have only 4 x 4" of total area to work with ... I don't think you'll achieve more than a few nF of total capacitance with that arrangement. Of course it will be very high quality capacitance, effective to very high frequencies, but realistically a factor of 2 difference in the capacitance value isn't going to make or break your design.
[Also, for stackup B] I fear that the signals are poorly shielded.
In either stackup your signal1 and signal4 traces aren't well shielded, and your signal2 and signal3 traces are fully enclosed by ground planes. I feel these two situations are essentially equal.
In a comment to another answer, you also mention,
I have many power source (+12V, +5V, +3.3V)
This means you'll likely need or want to break up your VCC "planes" between nets, and so there will be slots in those plane layers. That makes them much harder to use for return paths, as you do for signal1 and signal3 traces in stackup A.
Overall, I'd recommend stackup B.
Regarding the 1Vpp noise with the scobe probe ground connection but tip hanging out near the relay:
It is easy to induce noise onto a floating scope probe because they are very high impedance. Depending on the length of the probe ground wire, it's location, and the location of the probe, you are essentially making a nice pickup circuit for any kind of EMI.
Should you be worried about the proximity of the relay to your circuit? Two part answer-
Safety: Refer to IEC 60950 for safety related concerns in working with line powered circuits that you will want to sell or give to people. Also Underwriters Laboratories. There are required clearances you need to have that depend on your circuit and its application, so there is no way to provide an exact answer.
Functionality: If you have very high impedance circuits (> 1M-10Mohm) on your board that are arranged in such a way that they have some loop area that can be excited.
If all your stuff is digital (which generally low source impedance drivers), there is probably not a whole lot to be concerned about.
To demonstrate that, take a 100-1000 ohm resistor, solder one side to ground and leave the other side floating. Clip your probe ground to the ground side, and the probe to the floating side of the resistor. Now you have a signal (digital 0) with a source impedance of whatever the resistor is. Now flip your relay on and off, and you'll see how much 60Hz noise you will induce on some of your digital traces.
If you're taking some analog measurements (say a voltage measurement off a sensor), you need to be concerned about that sensor's effective source impedance along with any signal conditioning (filtering) you have. You could repeat the same test above but with the source impedance of the analog circuit.
In either of those situations, if the amount of noise is bad (the definition of which depends on your application) then you may need some shielding:
If you shield the relay, you will only (maybe) knock out 50/60Hz coming off it. It's very hard to keep 50/60 Hz off of anything because it's everywhere. Lights. Walls. Outlets. Equipment.
If you shield your circuit (or sensitive circuit areas), you will protect yourself from other environmental noise sources as well. Once again, you might not be able to knock out 50/60Hz noise from your analog measurements, so you may need to filter it out later.
Regarding trace width, unfortunately, it depends. Without knowing more details about the nature of the design (is there a ground plane? are the traces carrying DC power? do they need a characteristic impedance as part of a transmission line?) there isn't any way to answer that one.
Best Answer
Apart from the comment from winny you also have to make sure to respect the safety of the mains side 220 V. and the rest of the circuit. If you remain in doubt you could enclose the mains side on both side of the print in a metal box. This way you could kill two birds with one stone. Safety against accidental touching and less influence from noise.