I don't think there are any な-adj in the third sentence at all (only nouns, which function like な adjectives), に is used as a general location particle, and is not limited to actual places, the first clause in
"Chopsticks, in (in the form of a) paddle, is done"
"In the way of a paddle, chopsticks were being used." or "In place of a paddle, chosticks were used"
Unfortunately, it's nearly impossible to get a natural sounding translation in English as して is extremely context sensitive.
The second clause,
means, to go up the river.
There's no な adjectives there either, but there is を.
The 'pattern' you mention is actually just two distinct and separate grammar functions.
を is the direct object of the noun (chopsticks is done)
while a noun or な-adj is turned into an adverb-like function using に. There's not really an English equivalent here, as English does not merge adjectives and nouns together.
As for him, she is done (to happiness, in happiness, in the form of happiness)
"He does her happiness", "She is done by him to happiness"
ZはYをXにする is best interpreted as "Z does things that generally lead to Y being X"
部屋をきれいにしました does not have は, so Z is 'I' by context, and the meaning would be "I did things that generally led to room being clean"
箸を櫂にして uses a noun instead of a na adjective, but the gist of it is "(I) do things that generally makes the chopsticks to be a paddle"
(I) do things the generally makes the chopsticks to be a paddle, then went up the river.
I'm really terrible at formatting - can someone help me make the answer more readable?