Electronic – What causes that characteristic chirping noise in switching power supplies

Yes, it is true that adding a linear regulator after a SMPS (switch mode power supply) will reduce noise, but care is still needed. Results can be very good, but the result may not be as good as if a mains powered transformer plus linear regulator had been used.

Consider a common LM7805 5V regulatorfrom Fairchild. This has a "ripple rejection" specification of 62 dB minimum. "Ripple" is input noise but usually related to the twice mains frequency variations from the rectified and smoothed mains input. This is a reduction in noise of 10^(dB_noise_rejection/20) = 10^3.1 ~= 1250:1 That is, if there was 1 Volt of "ripple" at the input this would be reduced to 1 mV at the output. However this is specified as being at 120 Hz = twice USA mains frequency, and no specification or graph is given for noise reduction at higher frequencies.

The functionally identical LM340 5V regulator from NatSemi has a slightly better specification (68 dB minimum, 80 dB typical = 2500:1 to 10,000:1) at 120 Hz.
But NatSemi kindly also provide a graph of typical performance at higher frequencies (bottom left corner of page 8).

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It can be seen that for 5V output ripple rejection is down to 48dB at 100 kHz (=250:1). It can also be seen that it is falling about linearly at about 12 dB per decade (60 dB at 10 kHz, 48 dB at 100 kHz) . Extrapolating this to 1 MHz gives 36 dB noise rejection at 1 Mhz (~= 60:1 noise reduction.) There is no guarantee that this extension to 1 MHz is realistic but the real result will not be letter than this and should (probably) not be much worse.

As most (but not all) smps supplies operate in the 100 kHz to 1 MHz range one can guestimate that noise rejection will be in the order of 50:1 to 250:1 in the 100-1000 kHz range for fundamental noise frequencies. However, smps will have output at other than their fundamental switching frequency, often much higher. Very thin fast rising spikes which may occur on switching edges due o leakage inductance in transformers and similar will be less attenuated than lower frequency noise.

If you were using a smps by itself you would usually expect to provide some form of output filtering and using passive LC filters with a linear "post regulator will add to its performance.

You can get linear regulators with both better and worse ripple rejection than the LM340 - and the above shows you that two functionally identical ICs can have somewhat different specifications.

Noise elimination from smps will be greatly helped by good design. The subjct is too complex than to do more than mention it here but there is much good on this subject on the internet (and in past stack exchange replies). Factors include proper use of ground planes, separation, minimising area in current loops, not breaking current return paths, identifying high current flow paths and keeping them short and away from noise sensitive parts of the circuit (and much more).

So - yes, a linear regulator can help reduce smps output noise and it may be good enough to allow you to power audio ampliers directly this way (and may many designs do just that) but a linear regulator is not a "magic bullet" in this application and good design is still vital.

This depends on the type of laptop and power supply, some have additional logic signals, etc.

In all likelihood, your lab power supply is not able to provide enough current to power your laptop. Laptops use a good amount of power, if you have the original power supply it came with, you would see a current rating in mA or A. This is the total amperage the power supply can provide, and my guess is that it is at the least, 2 Amps or more. You may be able to charge the battery with your lab supply though.

There are other possibilities too, but without knowing the laptop model and the specs on your lab power supply, I couldn't say. Your lab supply may very well be able to power the laptop, however when the laptop is first turned on, your power supply may not be able to quickly adapt to the load.

the power supply is able to provide 3 Amps and the Current measurement shows that consume doesn't exceed 1.5 Amps

There are a lot of possibilities here, perhaps your lab supply isn't accurate or there were power fluctuations. Maybe your adapter plug was not the correct size, so you had a poor or intermittent connection. The laptop may have had an unrelated issue, that caused this problem, I've seen some that turn off as soon as you plug in external power. Perhaps the battery was bad, problem with the motherboard, or maybe a fan wasn't working. There are just a ton of possibilities.

the laptop is an old lenovo... "the beep and dead" seemed to be a power security act... HOW can the laptop distinguish between the its adapter

Usually a beep like that is a bios problem or warning. Also, according to this, it seems that Lenovo has different power supplies and depending on what one is used, it will throttle it's performance. A power supply for a laptop doesn't just have to provide power, sometimes there is some data communication/feed back, perhaps even just a way to verify that the power supply is a real brand name one.