Yes I'm sad enough to turn the possibly rhetorical questions to semi-realistic answers. Semi in this case meaning as far as I can stretch my scientific imagination. Also I'm going to ignore that Animorph's is just purely fictional so magical answers similar to it-just-does doesn't exist.
Do you men how do they flaten themselves/liquify to take control?
We know they can compress themselves (obviously to move around) it's possible that their bodies are highly compressible which suggests they can range from large to mini (smaller than an ear hole in width and height) which seems quite ludicrous. It's possible that their apparent large size (relative to an earhole) is mostly due to something that they can expel like some form of gas which would require some solid/liquid to gas conversion before shrinking to earhole size. The conversion is required otherwise their density would suggest they can virtually float in air or jump immense heights which apparently they can't.
To take control another theory is that only a small part of their body is the nucleus/brain and an extremity/limb of thin (possibly liquid as the books suggest) layer is extruded to filter through the brain crevices and intercept the synapses to redirect thoughts and actions. It would have to be either liquid or an immensely thin membrane to slip tendrils into all parts of the host brain.
how do they expell waste
What makes you assume that an alien race has to expel waste? Perhaps their recycling system is more advanced than our own. As with the first question some conversion could take place so that all waste are of small gaseous/liquid quantities so virtually any part of the body can be used to expel excretion. (Although I maybe talking complete ....)
how do they absorb Kandrona rays
How do you absorb x-rays, light/heat rays and any other wavelength of waves? The it-just-does argument comes to mind here actually hmm sorry. If the question is what Kandrona rays are then it's likely that it is some wavelength of light that is specific to Yeerks like how plants photosynthesise Yeerks kandrynthesise. Not a particularly specific question but it is my fault for picking it to try and answer!
how do they manage to avoid accidentally reproducing like amebas when they're pakced thousands into a pool?
This one I can't quite remember enough from the books to comment but presumably they're just like slugs or else they'd have some kind of uber baby boom. You can have a look at the wiki for slugs which at time of writing there are surprisingly more photos than are necessary (imo) and you might regret looking for it.
Thoughts? Other questions? Might have been a little pointless trying to explain how a fictional species can exist but in my defence this is a topic on Yeerk physiology and I like challenges when I'm a tad bored!