Use a potato ricer. Just fill it up with a big handful of spinach, and give it a good squeeze in the sink, or over a bowl if you like to drink spinach water. It extracts a ton of liquid quickly, and is a breeze to clean up when you are done.
Judging by the nutrition information I can easily find (for example, from nutritiondata.self.com), frozen spinach is generally cooked by boiling and draining. That's pretty much what I'd have guessed; it's certainly the easy way to cook things.
Unfortunately, that means that some nutrients are lost with the discarded water. I doubt it'd be different for any other green leafy vegetable - though it's certainly much harder to find frozen mustard greens!
The nutrition information for fresh spinach is for fresh, raw spinach; if you boiled and drained it, you'd make the same sacrifice that the frozen spinach has.
As for your generalization, freezing vegetables and fruits does preserve most things pretty well - but only what's actually left in them when they get frozen! And while transporting fresh vegetables around can cost you some "freshness", it's not going to affect minerals. Some vitamins could be lost by breaking down (I'm not an expert here, but it seems possible) since they're more complex molecules, but minerals are just single elements. Those iron atoms won't fall out of the spinach on the way, and they're certainly not going to be transmuted, either!
Edit: Essentially what's been said in the comments is that the USDA nutrition facts say that "Spinach, frozen, chopped or leaf, cooked, boiled, drained" has about half as much iron as "Spinach, cooked, boiled, drained". A discrepancy, indeed, though not the same one cited in the question. My interpretation here is that the frozen spinach is simply not cooked in the same way (boiled and drained more thoroughly) as the non-frozen.
An alternative, proposed by Adisak, is that the frozen spinach nutrition means that you've taken the already-cooked, frozen spinach and boiled it again and drained away even more nutrients. This seems unlikely; frozen spinach is already cooked, so there's no reason for the nutrition information to assume that you'll boil it over again. The description (it seems to me) is referring to the cooking that took place before it was frozen.
Best Answer
In my experience, stems can be rather stringy even after cooking. Likely varies by time of year, age/size of leaves, soil type, cultivar etc. Best adivice is probably to check a few stems (raw, steamed, whatever) and see. I always cut stems off at the base of the leaf, and have yet to have a complaint about the stem bits within the leaves.