The mic MUST have the same impedance (resistance) as the radios mic input (600 ohm - 1Kohm)
With RF (sch as the antenna circuit) that's true, but it's a bit different for audio.
With audio, the source (mic) needs to have a much lower
impedance than the load (radio).
Most mics are in the 50 to 750 ohm range, most radios are in the 5K to 10K range, so it usually works out OK.
Occasionally, you would get someone put a cheapie power mic on a radio with a lower impedance (such as the Cobra 148 or Uniden Grant) and wonder why the audio was so "tinny".
The ratio of output:input impedance is known as "damping factor" (google it and read the Wiki page if you have never heard of this term or you are not sure what it means).
A damping factor of less than 10 will result in frequency response shifts, and as you go towards a value of one, possibly oscillations and "ringing".
Damping factor is a figure usually used for audio power amps driving a speaker, but it applies equally when putting 2 amplifiers (i.e. the power mic and the radio) in series.
The bandwidth of the mike MUST be the same as the radio
Nearly all mikes will have a response far greater
than the radio - connect one to a CRO, use an audio generator to make some out-of-band tones such as 100Hz and 5Khz, and look at the pretty sine waves on the screen
Some Densi base mics have a response from 40Hz to 15Khz (hi-fi!).
This is actually a not an issue, all radios have a bandpass filter to only let through the voice (300-3000Hz) frequencies. The other frequencies picked up by the microphone will be discarded by the radio.
The output level of the mic MUST be set to the same output level as the origional radio mic
You can actually go quite a bit higher - there is a limiter in the radio that will reduce the gain to compensate.
Doing this raises the average signal level, which is useful for communicating with weak / DX stations.
Not so good sounding for the locals - that's what the gain adjustment / mic gain control is for...
Most limiters have a 30dB compression range - that's a 1000 to 1 range.
Even if your new mic has TEN times the output of the old one, you are still only using 1% of the available reduction of the limiter circuit.
most of the lower bass frequencies will not pass through the radio and will cause overload and even damage to these circuits
If they "do not pass through" how can they cause damage?
To go past the limiter capabilities of a typical radio, you'd need to go 1000 tines (30dB) past it's limit. Not likely in practice.
A typical mic can typically put out 25mV - this would need 25 volts
of audio to hit the limit - no mic amp would put out anywhere near 25V.
Of course, it you have done noob tricks such as disabling the limiter or putting in a so-called "swing kit" then part 3 does not apply