Yeah, that caterpillar doesn't have an annoying personality or anything. :p
The original of "You are old, Father William" is here, for comparison purposes. Personally, I think it sounds like a pretty damn boring life. :p
So now Alice is progressing from just eating and drinking strange things, to eating mushrooms suggested to her by caterpillars. This seems... natural? :p
Yeah, we won't go into Alice's odd bodily contortions and she shrinks and grows. Although I guess if different body parts grow/shrink at different rates... Not to mention how she could just nibble a bit at a piece of mushroom that she broke off and held in one hand when she was three inches high, now that she's above the trees... Unless they ALSO grow and shrink along with her.
Sorry, I know, I know. Too much logic for a fairy-tale, much like in Howl's Moving Castle. :p
For shame, Alice! Has no one taught you that eavesdropping is bad? (Although at this point, I'd probably be doing the same...) Not to mention just going up and speaking to Duchesses, after trespassing into their houses! And kidnapping, although in this particular case...
According to the annotations, "grinning like a Cheshire cat" was actually a phrase that was well-known before the books, so it's another pun/allusion, rather than just something created out of whole cloth.
I assume "nursing" the baby in this case means just holding it, comforting it, etc.
There are so many annotations to this chapter that I ended up just kind of glossing through most of them. One to the point, which may be known to everyone already, is that hatters actually did often go "mad" back in the day, due to mercury poisoning, since mercury was used in curing felt. Makes one wonder why anyone became a hatter in the first place, unless it was thought to just be coincidence.
And the schedule, if it's actually needed. :p