How long do seasons last

No. The only thing in the game that currently checks the weather, is the getWeatherMod function, in "calendar.js", which returns 0.15 (+15% bonus) during warm seasons, and -0.15 (-15% penalty) during cold ones. Note that weather only changes when the season changes, and is added to the season's own effects; a warm spring is thus +65% to catnip, and a cold winter is -90%.

The main section, above the census, is where you increase or decrease the number of kittens on a given job. You don't get fine-grained control over which kittens are doing which job, but you don't really need it; removing a kitten from a job using the [-] button always removes the kitten who is least skilled at it (of those working at that job right now), and adding a free kitten always adds the free kitten with the highest skill in it. As of 0.9.9.2, you can remove a specific kitten from their job when you unlock the Census, but assigning still always assigns the most-skilled kitten.

Note that your kittens can be skilled in more jobs than display, so you may not always be able to tell at a glance, but under most circumstances, your kittens shouldn't be changing jobs too often anyway.