Each of my three pens is green is correct.
You're thinking of each of as something that gets tacked onto the beginning of the noun. But when you add each of to my three pens, my three pens becomes the object of the preposition of. Each becomes the head of the subject. So the verb agrees with that, and each is always singular.
Of pretty much always does this:
The rumors were that she would leave him.
The gist of the rumors was that she would leave him.
Some nouns can be plural if they are followed by an of phrase with a plural object:
A number of flaws / A bunch of flaws / A total of ten flaws was found. (iffy)
A number of flaws / A bunch of flaws / A total of ten flaws were found. (ok)
but each isn’t one of them.
The meaning of each X is something like, “This sentence is true for every individual X”. This is clearest when you look at a sentence that is true of each individual, but not necessarily true of the group as a whole:
The roses cost $24. Each rose costs $2.
The terms "a countable noun" or "an uncountable noun" don't work well applied to given words, but rather to given uses. Note that those dictionaries that state whether a noun is countable, uncountable, or both, will often do so per sense rather than per lemma.
"The use of apple" would have been perfectly valid; it would apply to apple as a substance. Likewise "instead of pears" would also have been valid, referring to the fruit as individual, countable items, rather than as a substance. Indeed, some would disapprove of the sentence mixing the two different approaches; preferring either "apples instead of pears" or "apple instead of pear".
Hotel and situation are both being used as countable nouns, to modify the (countable) noun change to indicate what the change is of. In this case we use the singular because we need to change one hotel or one situation (that we need to change it for another hotel and situation respectively, does not affect this). If I was concerned with several hotels (say I was organising a conference and therefore had to deal with more than one) I might express a desire for "a change of hotels".
Even though we are using them as countable, we don't use an article, because of their modifying role. It's comparable to how we would say "a trouser press" (the article applies to press not to trouser) or "trouser presses" (no article because presses is plural, singular trouser used even though trousers is normally plural).
Much less formal, but less wordy: "There are five items in 4 different colors: one red, one yellow, one green, and two black."