Confusion in the Episode

[Davey]

Here are some questions about the episode, a lot of which escaped me. I watched several seasons of the show Sliders so I rather like the significance of parallel universes.

1) How did the Daedalus originally get where it was with the dead parallel crew?
2) McKay indicated that "our" team were the THIRD crew. So that makes the question even stronger.
3) Why didn't we get to know more about those neat aliens who crashed into the ship but survived to attack? They seemed to be part replicator, part Wraith, part human, with an electronic device blinking on the side of the heads. I was hoping that a live or dead alien would be able to get back to our universe for study and research. If they were in the parallel universe, they must be in ours in Pegasus as well.
4) How many potential permutations of Atlantis and Gang could there have been?
5) If parallel universes involved the same people, how did it happen that the dead Daedalus had a female commander, and what would have been the fate of the crew who beamed down to the planet?
6) Why didn't our Sheppard introduce himself to the other Sheppard?
7) I didn't clearly understand what McKay was trying to explain about the various drives. How could there have been a drive that got the ship into a parallel universe to begin with? Especially since he said there could potentially be millions of parallel universes?
8) How could the crew have been 100% certain that they were in our universe when they decided to jump ship and float in space waiting for Lorne to come and get them?!

[DigiFluid]

1) How did the Daedalus originally get where it was with the dead parallel crew?
They were hopping universes. They couldn't shut off the drive. They died, the ship kept hopping.

2) McKay indicated that "our" team were the THIRD crew. So that makes the question even stronger.
This is not a question.

3) Why didn't we get to know more about those neat aliens who crashed into the ship but survived to attack? They seemed to be part replicator, part Wraith, part human, with an electronic device blinking on the side of the heads. I was hoping that a live or dead alien would be able to get back to our universe for study and research. If they were in the parallel universe, they must be in ours in Pegasus as well.
For the same reason we never again saw the villains from the Season 5 mid-season two-parter (I'm being intentionally vague here because I don't know if you've seen it or not) or any other unresolved plot threads -- because the show got cancelled before they could follow up on that storyline.

4) How many potential permutations of Atlantis and Gang could there have been?
Infinite.

5) If parallel universes involved the same people, how did it happen that the dead Daedalus had a female commander, and what would have been the fate of the crew who beamed down to the planet?
It's a parallel universe. Anything is possible.

6) Why didn't our Sheppard introduce himself to the other Sheppard?
Awkwardness.

7) I didn't clearly understand what McKay was trying to explain about the various drives. How could there have been a drive that got the ship into a parallel universe to begin with? Especially since he said there could potentially be millions of parallel universes?
I don't understand what your issue here is? A version of Daedalus with the dimension-hopping drive was built in wherever its home universe was. It hopped through universes and happened to meet up with our universe's Atlantis crew. There's nothing to say this couldn't happen again; this Daedalus is just the one that was the subject of this episode.

8) How could the crew have been 100% certain that they were in our universe when they decided to jump ship and float in space waiting for Lorne to come and get them?!
Because as McKay said in the episode, the drive had a log of universes they've been through. If you're from universe D, and the log shows you hopping to E, F, and G before you shift it into reverse, you just hop out once you get as far back as D. The episode was very clear about this.

[Davey]

Then the question arises as to why our Atlantis team didn't develop an alternate reality drive and why the alternate McKay couldn't figure out what our McKay did. And it still should have been the case that the alternate Daedalus should have had the same commander as ours did.

[DigiFluid]

Then the question arises as to why our Atlantis team didn't develop an alternate reality drive
No it doesn't. Ours is one of an infinite number of parallel universes where an infinite number of possibilities happen. Their McKay had developed it, ours had not. Simple as.

and why the alternate McKay couldn't figure out what our McKay did
Our McKay could figure it out because the other McKay(s) didn't. It's essentially the scientific method to a tee -- 'x didn't work, y didn't work, but aha! z works!'

And it still should have been the case that the alternate Daedalus should have had the same commander as ours did
No it's not the case. The other Daedalus is from a parallel universe where similar but different things happened.

[StargateMillennium]

I think your confusion arises from not understanding the concept of alternate realities.
Alternate realities means that anything that can happen, will happen in another reality. Anything as small as a single chair on Earth being a little more to the left. To anything as big as completely different ppl existing throughout the entire universe.
If you want to get really extreme, the theory of alternate universes even suggests that maybe another universe can run on a different set of physics.

This is why Daedalus had a completely different commander. Why they had a Alternate Reality drive. Because it was possible for that to happen. And it was possible for that to have never happpened. So both scenarios happened in an alternate universe. It doesn't have to mirror ours (well, theirs).