Track muting

Is it possible to mute a track as an effect?
I have tried the amplify-effect to do this
but produces clicks sometimes.
(could use fade in/out or enveloper to prevent clicks
in my case that would require 100’s of
extra operations)

You can silence audio using “Edit menu > Remove Special > Silence Audio” (the keyboard shortcut is Ctrl+L).
Silencing the audio by this method or with the Amplify will cause a click if the start or end of the selection are at a point where silencing will cause an abrupt change in the waveform. If you choose your edit points with care, then you can avoid clicks.

“Good” edit points include:

You should also ensure that your recording has no “DC offset” before you start editing. See:

My mute selections are chunks with fixed time.
Pretty time consuming to select milliseconds.

Can I somewhere propose a new effect called ‘Mute’ or ‘Damp’.
3 parameters would be sufficient:
fade out time,fade in time, and attenuation (%)

and checkbox mute/unmute as reverse function to undo for editing
if possible.

Roughly how long are the sections that you want to mute?

An important difference between the track mute buttons and an “effect” is that the mute button does not change the audio data, it just tells Audacity to not play it, whereas effects change the audio data when the effect is applied. This means that if you “mute” part of a track by making it totally silent with an effect, then it is not reversible - the audio data is changed to silence when the effect is applied.

If you only want to reduce the level of the audio, then it could be reversible provided that the following conditions are met:

  1. The track must be 32-bit float format (the default in Audacity). Other formats are not precise enough to allow substantial amplification without some loss of sound quality.
  2. You must be able to select exactly the same audio to apply the reverse effect - not “nearly the same” audio, “exactly” the same audio.
  3. The settings for undoing must exactly match (complimentary) the settings when you applied the effect.

If these conditions are met, and the required selection is not too long, then a plug-in effect could be quite easily made to reduce the level by say 20 or 30 dB, then, provided that you can make exactly the same selection and set exactly the reverse settings, the effect can be reversed.

I don’t know audacity inside-out but IMHO keeping a multiplier per
32 bit float applied realtime would be better in this case then
multiplying before. Undoing then would only change the multiplier
while the track data remains unchanged.
Also enveloper, amplification fade effect and others could do this
what would not affect the audio resolution while editing doing and
undoing a 1000 times.

Audacity does not do real-time processing, it’s the wrong sort of program for that. Audacity is essentially a wave editor, albeit quite a fancy one.
There is an alternative approach that might suit your needs…

Audacity is designed to work with multiple tracks at the same time. The number of tracks it can handle depends on the hardware, but for most modern computers you can work with quite a lot of tracks. If you want to be able to silence some parts temporarily while listening to others, you can move parts to new tracks and then use the mute / solo buttons as required. A useful keyboard shortcut is Alt+Ctrl+i (“Edit menu > Clip Boundaries > Split New”