Usually puffy lids resolve after surgery. Often, pre-existing bags under the lids are more obvious without glasses to hide them.Before and after pictures would really be useful here.
The acrylic material of the most commonly used intra-ocular lenses has this cosmetic side effect.
Some people call it "Terminator Eye". The only way to get rid of this cosmetic issue is to exchange the lens for another one of different material. It's low risk but not now risk to...
Botox is a relatively safe procedure as is cataract surgery. Even though there is hardly any risk of systemic infection from botox injections I would not do it on the same day as cataract surgery and give a short period of time before hand. The very fine botox needle does pierce the skin...