What does "Water, is taught by thirst" have in common with "Success is counted sweetest?"

You have picked two excellent poems to compare and
contrast! Unfortunately your original question asked more than one question, so I have
had to edit it to just focus on the similarities between these two
poems.

Both of these poems are carefully built around
paradox. "Water, is taught by thirst" contains many paradoxes as Dickinson seems to be
pointing towards the paradoxical nature of so many aspects of
life:

Water,
is taught by thirst.

Land -- by the Oceans
passed.

Transport -- by throe
--

Peace -- by its battles told
--

Love, by Memorial Mold
--

Birds, by the
Snow.

Note how this list
shows how concrete nouns are defined often by their negatives - peace is defined by "its
battled told", for example. In the same way, in "Success is counted sweetest" the whole
poem is built around the fact that it is only those who "ne'er succeed" who can fully
understand success and count it "sweet." She offers us a scenario of a victorious army,
none of whom, we are assured, can understand the "definition / So clear of victory" as
the dying soldier who in his last moments hears the triumphant noises of the opposing
forces.

One of the remarkable aspects of Dickinson's poetry
is that she forces us to see concepts and ideas in completely different ways and often
uses paradoxes to present them and really make us think about the nature of such things
as "success."