555 is not that flexible, it has “fixed” thresholds and the output pulse is more the less the same as the supply voltage ..
However, you can do almost all what you’ve described with PICAXE-08 ..
Have a look at the attached picture .. it’s self-explanatory ..
P1 can be programmed to “read” the amplitude of the incoming signal, whereas P2 can be programmed to control the width of the output pulse ..
If you vary [V+], that’s the voltage that supplies the output driver, you can vary the “height” of the output pulse .. Rgds,
IanP