Does George Lucas mention Earth in "Star Wars"?

Famously from the opening credits of Star Wars it is set...

Essentially this is an equivalent to the fairy tale 'once upon a time' opening. It tells us that it's not really important where or when the story is set.

There are however exceptionally tenuous movie links to the Earth - in that you see creatures like E.T. in the Republic council meetings:

However this is barely more than an 'easter egg' than a true linking to Earth in the Star Wars universe. So I would have to conclude that the answer is 'no'.

Yes, although in all fairness more as a gag than as a serious canon fact. Then again, Jar-Jar Binks is a serious canon fact, so who am I to judge canon? :)

I have discussed the links in detail in my answer to "Are E.T. and Star Wars in the same universe?" SFF Q&A.

I shall now shamelessly borrow from that answer the way J.J. Abrams borrowed from Episode IV :)

TL;DR: Yes.

• As a gag/easter egg/cross-merchandizing/friendly jest/whatever, Spielberg and Lucas have placed enough canon information in their universes to imply that E.T. really is an alien from a species in a Star Wars Galaxy.

• E.T.'s species were officially called The Children of the Green Planet, their planet was called Brodo Asogi.

• In addition, as documented in my SFF answer to "Are Star Wars and Indiana Jones the same Universe?", there is a second mention: somehow, Indiana Jones's The Ark of the Covenant is strongly implied to originate fron... Han Solo's Episode VII cargo ship "Erevana":

  

  

Another "easter egg" type instance of things related to earth being included in the movie is the person in the potential Gemini/Mercury spacesuit in one scene.

Thread discussing it here: https://scifi.stackexchange.com/questions/80002/what-evidence-is-there-that-proves-disproves-there-was-a-gemini-earth-astronaut

But of course since this is a galaxy far away and a long long time ago this is more of a costume budget issue than an in-universe reference to Earth.

While the Battlestar Gallactica series did make reference to Earth that they didn't know if it existed or not, in Star Wars, never is Earth mentioned at all. That is different than saying that in the opening text it says "A long time ago, in a Galaxy far far away." One might say that at some other point earth is mentioned, but no, it is never mentioned.

Curiously, by saying "A long time ago, in a Galaxy far, far away..." it does imply an audience that is being addressed. So, it is told to an audience on Earth and the events happened a long time ago from our point of view and a Galaxy far from us. Still, in no way does the movie ever make reference to Earth at all.

Several characters in Episode I refer to humans - C3PO ("human-cyborg relations"), Anakin ("I'm the only human who can do it"), and a pod race announcer ("that little human being is out of his mind"). This is not a direct mention of Earth but Earth may well be an origin of humans.

Implicitly, yes.

A long time ago, in a galaxy far, far away...

This pins the events of Star Wars as occurring "a long time" before 1977 and in the same universe as Earth, albeit in another galaxy that is "far, far away." A long time and far away are both subjective measures, but we can at least infer that the events are occurring in a different galaxy than the Milky Way. This could well be the nearest galaxy to us: the Andromeda Galaxy, which is about 2.5 million light years away. Certainly that is far, far away... though by galactic standards, it's our next door neighbor. The farthest known galaxy is 13 billion light years away, which by comparison makes 2.5 million light years not so far.

In any event, the very first words on the screen reference the events of the film in relation to Earth and the year 1977.

In the movies, there was no direct mention of earth. So the answer to your movie-related question is "No".

But in the expanded universe, there were mentioned, that the Rakatan Empire found humans on some planet and spread them around the whole universe, but it was not the earth. So in the movies, there is no direct answer where do humans come from, but in the extended universe, it is clearly stated, that humans are not from earth.