1. Mr Palmer's house in Town is in Hanover Square, a section of London that wasn't built up at all in the early 1700s. This means that as these things go, his house is in a relatively new section of the city, and one that was largely inhabited by Tories - people who supported King George. It's name comes from the House of Hanover, the German family name of King George, and the highly sought-after and prestigious St George's Church is located there - it's where the most fashionable marriages among the Ton were performed.
This means, of course, that the Palmers are quite well-off and well-connected (something we will learn more about later, when we learn that Mr Palmer is running for Parliament - I don't consider it a spoiler since it doesn't really impact any of our main story lines). It also means that they are likely Tories (Austen certainly was).
2. Charlotte Palmer is very kind-hearted and extremely social, but vapid. She has taken an instant liking to the Dashwoods (one assumes she's not overly particular, which will be borne out), and she wants to spend time with them and know them better. She invites them to take a house in Town, probably not thinking about the financial implications of that at all. No way the Dashwoods can afford any house in Town (although perhaps they might swing lodgings, but that's a moot point), let alone one in such a posh neighborhood.
She later invites them to visit their country home, Cleveland, at Christmas time. The Dashwoods decline (again) because they simply don't want to go (same reason they truly decline the London proposition), not because they don't want to be away at Christmas time. Christmas was not nearly the "time for family" that it's become in the years since the Regency, and it was not unusual for people to go visiting during the holidays; in fact, it was rather a common course of action.
She then declares that she has heard in Town that Marianne and Willoughby are engaged - although truly, her mother hinted at it in a letter, and nobody has confirmed it for her. She ran into Colonel Brandon and asked him about it, but he didn't actually answer her inquiry - indeed, I rather expect that the proper way of characterizing what has occurred is that Colonel Brandon has heard about the engagement in Town, and not the other way around.
3. Charlotte Palmer acts within the bounds of propriety. Even though she's knocked up, she offers to chaperon Elinor and Marianne in London if their mother doesn't want to go out. Her offer is based on her knowledge that Mrs Dashwood hasn't been a widow for a full year yet, and while the deepest mourning period would have been considered over, it was common for some widows to stay out of society functions for a full year. Charlotte is aware, however, that she can only chaperon up until the point where she is confined - meaning until she goes into labor or has to take to her bed for some pregnancy-related reason.
Mr Palmer is a curmudgeon, but he often speaks the truth.
Although often described as 'comical' or 'droll' by his wife, Mr John Palmer is generally unpleasant within the book. That said, his character is actually 'comical' or 'droll' to most readers. He's grumpy because it rains, finds his (admittedly chatty) wife annoying, and resents not having something to do indoors to while away the time (besides reading his newspaper, which he enjoys, or engaging with other people, which he only likes on his own terms).
1. He calls Sir John "stupid," probably meaning that he's in need of common sense, and not that he's actually unintelligent. We are meant to infer that Mr Palmer is a plain-speaker, and not necessarily that he's unuterrably rude, even though that's an interpretation one is free to make. We've all spent time with Sir John already, and we know he can be as high-spirited and chatty as Mrs Palmer and that, although good-natured, he's lacking in seriousness.
2. He's stuck with Charlotte. It's hard to remain completely unhappy with Mr Palmer when he starts correcting his wife about Willoughby's home at Combe Magna (that first word is pronounced as if it were COOM, btw), because it doesn't take much to see that Charlotte has little idea what she's talking about - not that she lets that stop her, of course.
3. He then calls Mrs Jennings "low-bred", and Charlotte calls him out for being rude. He doesn't apologize, exactly, but he displays his complete lack of understanding of how other people might perceive him. And Mrs Jennings, bless her, doesn't take offense - she laughs at him and says my favorite line from this chapter: ''"Ay, you may abuse me as you please," said the good-natured old lady, "you have taken Charlotte off my hands, and cannot give her back again. So there I have the whip hand of you."
Two things: First, as we will see later in the book (through implication), Mrs Jennings is in fact not high-bred; her husband made his fortune in trade, and her daughters were able to "catch" well-positioned husbands because they were wealthy. So there's some truth to Mr Palmer's statement. Second, an explanation of the term "whip hand": it's the hand holding the whip while driving a coach, the one perceived as holding all the power. Mrs Jennings is saying she's the one with the advantage here, since now that Mr Palmer has married Charlotte, he's stuck with her and she's no longer Mrs Jennings's problem. Bless.
4. He is actually mannerly (in his way) toward the Dashwood sisters. He's clearly not shy about correcting or opposing his wife when she is wrong or when he disagrees with her. So when she invites them to Cleveland and asks him if he doesn't "long for them to come to Cleveland", he doesn't deny it. Instead, he gives something close to a ringing endorsement to the idea. And when Charlotte later says that he's quite taken with the Misses Dashwood, it seems unlikely that she's wrong. Although she is singularly amused by her husband's manners (proving the old adage that there's a lid for every pot), she is probably not mistaken in her assessment that he likes the Dashwoods, and that will later be borne out.
As readers we are meant to find Mr Palmer slightly off-putting, and I daresay most readers do, even though we understand why he doesn't enjoy meaningless conversation with frivolous people. The two things that keep him comical are, in my opinion, that he mostly limits his curmudgeonly comments to other comical characters who are essentially foolish, so his lack of patience is somewhat understandable, and that we have Elinor's insight into the fact that he's not nearly as awful as he makes himself out to be.
Dudes, I have an uncle just like that. He refers to himself as "the grump", and he's really fond of his rep as a bit of a curmudgeon. Underneath that? SUCH a nice guy. Would do anything for you. Just wants to be left alone to read his books and listen to his opera CDs and such without being constantly pestered by people, and once upon a time my aunt and cousins were the queen and princesses of pester. Hence the development of the reputation of which he's so proud.
Same goes for Elinor, whose observations we are privy to - she notes that he's married to a very silly woman (shades of Mr Bennet from Pride and Prejudice!), but that the reason for his acting in the way he does is out of a sense of inferiority/desire to be perceived as superior. Way to go,
Willoughby is a Whig
Charlotte explains that Mr Palmer doesn't call on Willoughby overly much, despite them living in the same county and despite Mr Palmer's Parliamentary aspirations, because Willoughby belongs to the opposing party. As we've already been able to ascertain from other things Mrs Palmer has said that her husband is a Tory, this makes Willoughby a Whig - and I am sorry to tell you that this does not bode well for him. Austen and her entire family were staunch Tories. However, Austen really didn't care for the Prince Regent with his extravagant lifestyle and his loose morals and his treatment (some would say mistreatment) of his wife - as well as his tendency to pal around with noted Whigs. I'm just saying, Willoughby's being a Whig doesn't seem to be an issue for Elinor, but I can assure you it is not perceived as a positive by Jane Austen.