“A woman’s hat designed to resemble a turban” (OED). This was a fashionable headdress for women from the 1790's through the 1820's, inspired by English trade with India (Walford, Vintage Fashion Guild).

According to the American Kennel Club, The Newfoundland is a massive breed of English working dog, used for pulling nets, carts, and carrying loads. Newfoundlands also make excellent guard dogs. Henry's puppy would look something like this,

but would grow to be a very large dog.

Terrier is a group of breeds, originally bred to hunt vermin. Some examples include the West Highland White Terrier, Cairn Terrier, and Norfolk Terrier.

These dogs were kept not only as companions, but as useful parts of the household: the Terriers to control rats and other vermin, and the Newfoundland (when grown) for protection and labor. Even so, the Newfoundland’s sweet disposition would make for an ideal companion (American Kennel Club).

"Boastful or inflated talk or behavior." Also spelled rodomontade, it is pronounced rädəmənˈtād (OED).

"A private conversation between two people" (OED).

"A member of the clergy engaged as assistant to a vicar, rector, or parish priest", or "A minister with pastoral responsibility" (OED). In this context, Henry either has engagements (appointments) to keep with his assistant, or he has engagements (duties) of his own as a clergyman.