Meaning of seal and engraved characters on teapot
For the seal identification portion, as mentioned elsewhere, the characters are 汪寅仙製 (meaning made by 汪寅仙, a very famous Chinese ceramics artist who passed away earlier this year; whether it's really made by 汪寅仙 is another story, as many of these pieces are actually fakes).

「寅」is fairly recognisable in this carving, so I'll provide a breakdown of the other three characters.

This carved seal is slightly more difficult to read than normal, because of the characters being squashed into a circular shape, causing some components to be slightly distorted.



汪


  「汪」is a description of a body of water meaning vast and deep, and is comprised of
  
  
  「氵/水」, a semantic component;
  「㞷」simplified to「王」, a phonetic component.
  
  
  
  
  「水」originally depicted flowing water:
  
  
  
  This directly leads to the seal script form 
  
  
  
  Note that the modern component form「氵」is a drastically simplified version, and ancient scripts did not write this component in this manner for a long time.
  
  
  
  「㞷」was the original character for「往」, and was a compound of
  
  
  「之」(to go), a semantic component, itself a compound of
  
  
  「止」(a depiction of a foot), a semantic component, and
  「一」(an abstraction of the ground), a semantic component
  
  「土」(a depiction of a lump of earth on the ground, meaning soil), a semantic component.
  
  
  The total form emphasises the meaning to go (by travelling on foot covering ground distance).
  
  「之」originally looked like
  
  
  
  and an ancestral variant of「之」looked like「㞢」; the following is a few samples of the shape to provide an idea of the relation between the shapes:
  
  
  
  「土」originally looked like
  
  
  
  but it was subject to some shape changes:
  
  
  
  A similar change actually happened to「十」, which morphed almost exactly like the top part of「土」. Note that these are not strictly how the character evolved, so don't over-interpret these sequences.
  
  The original forms lead to the combination
  
  
  
  and the shape of「㞷」should be seen as coming directly from「㞢」and「土」. This directly leads on to the seal script shape
  
  
  
  Note that the top-right part of this component in the original image is cut off to fit inside the circle.




仙


  「仙」is comprised of
  
  
  「亻/人」, a semantic component;
  「山」, a phonetic component.
  
  
  
  
  「人」is a side view of a standing person:
  
  
  
  This directly leads on to the seal script shape
  
  
  
  Note that the left side of this component is distorted to fit inside the circle.
  
  
  
  「山」was originally a depiction of mountain peaks:
  
  
  
  The side peaks eventually simplified into vertical lines, leaving the middle peak in seal script:
  
  




製


  「製」is comprised of
  
  
  「制」(originally to chop wood), both a semantic and phonetic component, itself comprised of
  
  
  「未」(the fragrant smell of a blooming tree (now written「味」)), a semantic component;
  「刂/刀」(a blade, indicating the meaning to cut), a semantic component.
  
  「衣」(clothes), a semantic component.
  
  
  
  
  「未」originally depicted a tree「木」with extra branches, representing blooming, and by extension the fragrance of blooming trees:
  
  
  
  For stylistic reasons, the bottom of「未」(and similarly 木, 本, ...) morphed into something resembling「巾」, leading to the seal script form
  
  
  
  Extras:
  
  
  In modern regular script, the bottom of 木 and 本 didn't retain「巾」, while「制」did retain this shape.
  In「制」,「未」is just used for its shape as a tree, not its meaning of「味」(fragrance).
  
  
  
  
  「刀」was originally a picture of a knife or blade:
  
  
  
  This directly leads on to the seal script form
  
  
  
  
  
  「衣」was originally a picture of clothing:
  
  
  
  This directly leads on to the seal script form
  
  




To summarise: