If the cage is T-300 type SS it will not rust. You can check with a magnet, it should not stick if it is a good cage.
Yes but... lots of things are non-magnetic including polished aluminum or ones chrome coated. And there are several varieties of pretty rust resistant stainless steel that are magnetic. A LOT of kitchen stainless is attracted to magnets (indeed must be to work with induction), though in some that's from different types of layers not innate throughout.
I wish it was that simple to tell good stainless from bad. Some manufacturers will tell you the stainless type (if they tell the truth, as so very many do not especially cheap imports). I could not find the type of stainless used by prevue for example, and I'm not knowledgeable enough about metals to tell (a magnet does not stick to it however). I bought it from Chewy who says it is 201 stainless (why would they say but not the manufacturer? Did they make it up, or are they right?). 201 is not as good as 304 but is a lot cheaper so it might be. 201 is not bad, just not as good as others.
I think the best bet to knowing its quality stainless is to buy from a brand with a reputation on the line, and be suspicious of the alphabet soup of brands coming out of china on Amazon (etc).
I think also how much it's worth spending for quality depends on the use case. A cage frequently outdoors near a chlorine pool or near an ocean with salt spray is very different from an occasional use cage inside in climate controlled space - and all that space in between those extremes.
And remember the correct wording of the old saying: "You do not get what you do not pay for"