are there nouns that can function as another part of speech?

Many English words have their definitions change depending on their parts of speech:

"type" (noun) = classification of something. (verb) = to peck-away as a keyboard.
"blue" (noun) = a color. (adj) = depressed, melancholy.

...

But, in the case of Japanese、are there any nouns that can also function as another part of speech? サ変動詞 do not count.

Answer

To some degree, 形容動詞 can flip between nouns and adjectives, but this is largely due to the fact that the morphology is nearly identical (the one difference is である vs な for modifying other nouns). There is also a very small number of loan nouns that already look like verbs and so are slangishly used as verbs (e.g. ググル＞ググる).

Beyond those, zero-derivation pretty much never happens. The reason for this is primarily the fact that most kinds of words are required to have a certain form even in an uninflected state - for example, verbs have to end with -u (and the number of consonants before that is restricted, you can't have -yu), 形容詞 have to end in -Vi, etc. This is why する has to be added to most nouns to make verbs - not because it's required to explicitly mark nouns being used as verbs, but because most nouns can't be used as verbs as they lack the proper form.

(also, your English examples aren't really the best - something better might be 'table', where the noun and verb definitions are clearly related (i.e. it's not just homophony, like 'type' and 'type').)