What does Gulliver mention about the doctors and habits of the people from his country?
Gulliver mentions that he himself was the doctor or surgeon aboard his ship and a physician by training. However, he does not paint a flattering portrait of his profession or the training that goes with it, using the habits and attitudes of people from far-away places to satirize the weaknesses, evils, and absurdities of the English.
At the Academy of Lagado, he describes a "great physician" treating a dog for colic by putting a "great pair of bellows ...eight inches up the anus...." The dog dies, and naive Gulliver leaves the reader to determine the competency of this particular famous physician, though there is little doubt he is entirely incompetent--and not much different, as we shall see, from learned physicians in England. At the same Academy, another doctor discusses various medical cures, including brain surgery, to make for better governance by legislators and kings (this is doubtless also advice that Swift thinks could apply to England's political class).
However, it is when he converses with the Houyhnhnms that Gulliver describes in some detail habits in England. He notes that in England doctors are needed not because humans are naturally sickly but because of overeating and drinking, prostitution spreading venereal diseases, and imaginary illnesses invented by the doctors themselves. As with the doctor at the Academy of Lagado, forms of enemas are a chief way English doctors "cure" illness: we can only imagine this treatment is about as effective as at Lagado. Gulliver also suggests that doctors murder rather than cure patients to save face when a person they had pronounced terminal begins to recover or when it is convenient (and by implication profitable) to get rid of someone:
They are likewise of special use to husbands and wives who are grown weary of their mates; to eldest sons, to great ministers of state, and often to princes.
As always, Swift uses Gulliver to point out what is wrong with the supposedly civilized England.
Gulliver (ironically) attempts to educate most of the groups with which he comes in contact about the superior nature of his own native civilization in England, and he does likewise with the Houyhnhnms until he comes to the conclusion that they are actually the more advanced race. He explains that, at home, his countrymen are subject to many different diseases, most often caused by their own behaviors: eating too much, drinking lots of alcohol, lack of exercise, insufficient sleep, and so on.
Further, he says that the women are always sick, sometimes suffering from "imaginary" diseases for which doctors have invented "imaginary Cures." Most shockingly, he says that when doctors have declared that someone is unlikely to recover from an illness, and then that person does begin to get better, doctors know "how to approve their Sagacity to the World by a seasonable Dose." In other words, he says, doctors are willing to poison someone when they've predicted the patient's death so that they retain their own credibility! How he could ever believe that such a country is superior to any other is certainly ironic, and he soon comes to believe that the Houyhnhnms are truly more mature and civilized than England.