I have been getting confused with these two ways of creating nouns and been wondering if there's any differences between them.
For instance, are the following sentences correct or not?
Don't try to freely create nouns from 連用形. There are many nouns that look the same as the 連用形 of the corresponding verbs, but such nouns were lexicalized long ago, and they often have different meanings derived from the original verb. You have to look up a dictionary each time.
見【み】 as a noun is found in certain fixed words such as 花見【はなみ】 (cherry watching) or 月見【つきみ】 (moon watching), but 見 itself is not a noun which means 'watching' in general. (e.g. you can't say 映画見 or 映画を見). 言い, 聞き, 食べ and so on do not work as standalone nouns, either.
Therefore 「映画を見るのが好きだ」 is correct, but 「映画を見が好きだ」 is ungrammatical. 「映画を見るのに行った」 is highly unnatural or probably ungrammatical, too.