Why mention (in Gen 2:1) “and all the host of them” in addition to “the heavens and the earth,” as the things created? The heavens and earth includes everything, no?

The word, צְבָאָֽם or tsaba, means literally “the host of them,” as the literal translations have it; the word means something like “armies.” But, obviously, since we are not talking about soldiers but merely every created thing, the word means something metaphorical. If it is to be contrasted with “heavens and earth” (וְהַשָּׁמַ֥יִם הָאָ֖רֶץ, hashsāmayim wuhā’āretz), then this “host” must mean the contents of (the items within) the creation; so then “heavens and earth” would mean the spaces and their structure. This is confirmed by a reference back to Gen 2 that occurs in the Ten Commandments at Ex 20:11: the Lord made “heaven and earth…and all that in them is.” This also precisely contrasts with Gen 1:2, which said the world was “without form, and void.”

God, being the source of all, is surely not in need of rest; being limitless, it seems he could do anything without effort. Why, then, does the text say in Gen 2:2 that he “rested”?

Indeed, it is very probably not because he needed a rest. Probably, the traditional explanation is correct: he was demonstrating to mankind what man should do: observe the sabbath, the weekly day off. The following sentence underscores this. The text anthropomorphizes God in this way, in a few different places, e.g., when it says “repents” and is “grieved” that he made man, on Gen 6:6. There are also physical anthropomorphisms; perhaps indeed God has no literal “face,” despite being said to have one (e.g., Lev 20:6).

What might be “holy” about resting (Gen 2:3)?

Perhaps nothing in itself. Certainly not every time a man rests is it a holy rest. But this demonstrated instance of resting was a holy example to man, who even before the Fall, here, is said to need one day in seven to rest. Insofar the day is set apart (the word for “holy,” קָדַשׁ or qadash, means something like “set apart”) from the other six unto God, and insofar as holy God himself “rested,” it makes sense that the Mosaic code, in the Ten Commandments itself, sets the sabbath as a holy requirement (Ex 20:8-11). Indeed, in the Decalogue, the text points back to God’s rest: “For in six days the Lord made heaven and earth, the sea, and all that in them is, and rested the seventh day: wherefore the Lord blessed the sabbath day, and hallowed it.”