im working on a mostly earthlike planet (aside from atmosphere) have a sky that looks green at noon to humans and pink during a sunset? could it be done via airborne algae? would the atmosphere still be breathable to humans?
Firstly, the star hitting that system could just not emit as much blue light, resulting in the next color being more diffracted (and more visible) than blue. This has some downsides, such as blue things appearing black or very much darker than here on earth. If you went the route of having a less hot star or a star with significant amounts of certain elements, you could get a mostly-green emission spectrum. (The less intense heat can cause an issue here, though!)
Secondly, as you point out, you could simply have something in the atmosphere that reflects more green than blue. This has the added bonus of letting blue items remain visibly blue.
For instance, Algae are noted to be frequently green and occur in blooms- but then you simply have the problem of how they get their nutrients and stay aloft! It does seem reasonable that some enterprising micro-organism stumbles upon a way to ride the wind - they experience a much different Reynolds number than we do!
Finally, pink/red skies often happen because of particulates in the air. These conditions happen on earth already! You see odd colors of sunset when storm systems, large forest fires, or other particulates in the air are west of you during sunset.
is there any way to make an earthlike planet (aside from the atmosphere) have a green sky at noon and a pink sky at dusk
would the atmosphere still be breathable to humans?
Roughly speaking, the oceans were anoxic and filled with an interesting bacteria soup rich with sulphate-reducing bacteria and purple sulphur bacteria. The former group thrive in the oxygen-free oceans and generate vast quantities of deadly hydrogen sulphide. It filles the air and wrecks the ozone layer. Ward suggests that the concentration of the gas in the atmosphere results in a greenish sky, though I must confess I haven't been able to find any supporting evidence for that claim or how he worked it out.
The ocean surface is covered with a thick mat of the purple sulphur bacteria who photosynthesise and consume some of the hydrogen sulphide reducing it to elemental sulphur but producing no oxygen.
The colour of the Earth's surface often has influence on the colour of the sky and clouds above it, and certainly an ocean sunset on such a world would be pretty pinky-purple.
So! If Ward was right, not only is your world possible, but it has happened before and if the most pessimistic models of destructive climate change come true, it can happen again! It just isn't really somewhere that people are really going to want to visit, and not much is going to live there.
Every day after dawn, vast hordes of insect-like creatures with green-tinted, diaphanous wings fly up beyond the cloud layer to soak in the sunlight. The green in their wings is chlorophyll, and the sunlight helps them break down nutrients they have eaten through the night. In the evening, when sunlight fades, they descend to the ground to feed through the night, leaving the sky clear for a typical pink sunset. Their shit and decaying bodies fertilize the ground. It is a sort of symbiosis where plants get the use of photosynthesis secondhand instead of firsthand. Imagine plants sending their leaves up in the air to gather sunlight, and you're not far off. This symbiosis may have evolved because thick cloud layers often block out the sunlight or have in the past.