Why did Cloud want to take the Huge Materia?

1. If Shinra is attempting to destroy Meteor at this point, why does Cloud (you) want to stop them? I know that while on the rocket, Cloud makes some comment about how the Huge Materia is too special / important to lose it, but Shinra is attempting to save the entire Planet at this point.

I believe the comment you are referencing is when Cloud says, on the rocket ship:

Hey, Cid! What're you doing!?
There are generations of knowledge and wisdom inside the Materia.
We're gonna borrow their powers and save the planet from Sephiroth.
There's no way that we can lose the Huge Materia. You understand that, right?

He does have a point; that Huge Materia can indeed be useful. You can use it to get Bahamut ZERO and to get Master Materia.

But Cloud is in no condition to make decisions when the team first starts taking the Huge Materia from Shinra. It's actually Barret who first says:

Can't let Shinra get a hold of the Huge Materia!

Barret of all people is not inclined to go along with Shinra; he's been bombing their reactors, he thinks they are killing the Planet, and they just tried to execute him. So trying to stop whatever they're doing is automatic for him.

Also, consider how the team even knows about this plan. They were tipped off by Cait Sith/Reeve. Reeve designs Mako reactors; he presumably knows a lot about Mako/Materia and would know whether the plan had a reasonable chance of succeeding. The fact that he tips off the team about this plan and doesn't say a word supporting it likely means that he (correctly) doesn't think it will work.

2. Why did Shinra still launch the rocket anyway if they didn't have all the Huge Materia to put on board as they planned?

At that point they do still have one Huge Materia to put on the rocket - they've already collected the Huge Materia from Nibelhiem before you learn about their plan. (This is the one you can steal while on the rocket.) Think about the situation when they launch. Meteor is so close that it's prominent in the sky. Your party has already shown themselves capable of holding off the Turks, so them recapturing it from you in time doesn't seem likely - indeed, it's more likely that the one they still have will be stolen too if they delay. And they know the disaster that will happen if they do nothing. So why not launch it with the one Huge Materia and hope that's enough?

3. Is there an in-game explanation why it doesn't matter if you succeed in getting the Huge Materia or not? If you fail to get the Huge Materia in the mini-games during that part of the game; then wouldn't Shinra have put the Huge Materia on the rocket? Wasn't the whole point that the Huge Materia was the only thing they knew of capable of destroying Meteor?

It simply doesn't work. It turns out that throwing Materia at a giant meteor doesn't destroy it. Meteor does appear to take some damage whether or not the Huge Materia is present; maybe that's due to a bunch of extra rocket fuel exploding or something.