Your examples are heterogeneous. They do not form a natural kind. Let's take them one by one.
Washing the Dishes / Dashing the Wishes
is an example of a spoonerism, that is,
a verbal error in which a speaker accidentally transposes the initial sounds or letters of two or more words, often to humorous effect.
Spoonerisms are typically speech errors, but the term can be used more broadly to mean an orthographic transposition that might even affect pronunciation.
Next,
Washing the Dishes / Wishing the Dashes
might be called an intra-word spoonerism, that is, the transposition of sounds or letters within two words.
Washing the Dishes / Flushing the fishes
is an example of multi-syllable rhyme where the first pair "washing/flushing" are only slant rhymed. The second pair "dishes/fishes" are full rhymed.
Making Breakfast / Braking Makefast
is another example of a spoonerism.
Go to the Shop / Sho to the Gop
is also an example of a spoonerism.
Go to the Shop / Flow to the Drop
is another example of multi-syllable rhyme. Here, the pairs are comprised of full rhymes ("go/flow" and "shop/drop").