1. The ship has not been fully explored yet. Nor has the controls Rush has been fully defined as well, so we don't know the answer to that.
Does anything about the layout or structure of the ship so far looked like a high-security prison facility? Look at the gate room, which would be the main place prisoners would board the ship. It doesn't exactly look like the kind of place you would want to do a transfer of dangerous prisoners. If the Destiny was a prison ship, wouldn't there be bottlenecks where the prisoners could be scanned/searched and more obvious security measures?
2. If there were guards, it would be for them in order to defend against people who would want to liberate the prisoners on board the ship. Plus, you also want to protect your people against hostile races anyway. Of course you could make an argument that the shields should be much more powerful and nigh impregnable.
Ideally, you wouldn't put the guns on the ship the prisoners were on. You would put the guns on escort ships the prisoners wouldn't have access to. That way, you would have the added advantage of being able to blow up the prison ship if the prisoners got loose.
3. The Ancients are an extremely advanced society. So this may be the equivalent of a low tech power to them. Plus, why make it easy for prisoners to escape in the first place? You don't really want them returning to society do you? Plus, these are the Ancients we're dealing with, so there's no way on knowing what their particular style of philosphy is and their reasoning behind this, at least for now.
Okay, the Destiny is obviously less technologically advanced than Atlantis. We know that Atlantis was far enough away from Earth that it was impossible for the Stargate network to connect the two without using tricks or Zero-Point-Modules (the most advanced energy storage device used by the Ancients in their more advanced technology). So we know that it took a considerable amount of power for the ancients at the height of their technology to open a Stargate between two nearby galaxies. So what evidence is there in Stargate canon that it was possible for the ancients to casually open a Stargate to something unthinkably further away, during a time when the ancients were less technologically advanced?
4. Well, who says they're being sent out to explore? Perhaps they're being sent out to a distant penal colony of some sort. There are historical precendents for this as well.
All evidence in the series points towards The Destiny being the core of a fleet of ships that have traveled far beyond where anyone from the Milky Way has ever set foot. If there was a Penal Colony there were heading to. They would have reached it a few thousand (million? I forget the numbers they mentioned in the first episode) years prior. ELi and Rush would have noticed it in the planetary database too.
To be honest, your entire theory is pretty silly. It is based on how harsh the situation on the Destiney is, and that in your opinion Rush is a liar; however, it is contradicted by just about everything in the series itself. I suggest thinking through the information the show has presented to us again.
Besides, if a space-faring society wanted to lock someone up and through away the key, why don't they just maroon them on a random planet? If the Destiny
was a prison ship, I would feel compelled to wonder what the writers were thinking.