Hello there.
In regards to the day counter:
With default settings 9 days account for a month in game, there are 12 months and 4 seasons which last more or less 3 months each just like irl, keep in mind temperature may vary wildly depending on your map position.
You first spawn in a new world the day 1st of May which is the last month of spring if I am not mistaken, a month after that and you jump to summer, with this info you'll just have to do the math to figure out season and total days lived in world. There are also mods that show exactly what season you are in, like this one https://https://mods.vintagestory.at/simplehudclockpatch
And In regards to the bears climbing ladders:
Someone else might have to correct me but as far as I know bears CAN climb them, most bears you'll meet playing on regular settings can also climb up to 3 blocks of any type so bear that in mind.