Technically you could use a pair of rods to fly, you don't need a wall even. Just lock one three feet in the air, and climb on it to put the next at 6 feet. On and on, as high as you want.
Not a lot of room for balancing, and you'd have to balance on one rod while you reached back and picked up the previous one. It'd certainly be easier to achieve if you had opposable thumbs on your feet, or a prehensile tail capable of pressing the button. Or Mage Hand I guess.
You don't need to penetrate rock, that's only used to secure the rods normally and well...
True. You'd still need some climbing checks and fatigue checks though.
Incorrect. restrained is not incapacitated. Restrained gives you a speed of 0, advantage to hit you and disadvantage on dex saves. So this does not in any way stop you from hitting the button on an immovable rod (although, wow! what a button that it takes 6 seconds to press!).
See: misunderstanding the rules. Happens to everyone.
I suppose it also begs the question: does the Rod secure itsself in a fixed 3-dimensional point in space? Or is it relative to the user? The nearest large gravity well? Does the Rod know when it's inside a larger object? Could you use an Immovable Rod on the Moon to stop its orbit, or would it lock itsself to a fixed point relative to the Moon? Would an Immovable Rod placed 250,000 miles from Earth still rotate with it or would it stay fixed in that point of space? Wouldn't a
truly Immovable Rod be immune to the forces of gravity and the moment you lock it in place you would suddenly realize you're hurtling through space at 18mps and spinning on a top at over a thousand mph? Wouldn't it be more accurate now to call it a "Rod of Relativistic Positioning"?
Even if the Rod is in a dragon's stomach, I would think the physical force of the dragon's mass (given it was large enough to swallow an average humanoid whole) moving would overcome a DC30 Str check.
The real way that this one is not a problem is simply that monsters which swallow you are quite rare, and even if you do meet them, they typically swallow only one member of the party, and the likelihood of that being the guy with the immovable rod(s) is slim. And even then, if they can swallow you + rod, it's not inconceivable that they can simply regurgitate the rod.
Right, not to mention you also have to ya know, probably
die in order to accomplish this. So I guess as a heroic sacrifice against an enemy this might be interesting, but I think Agent K probably had a better idea of being swallowed with a really big gun.
In short, if immovable rods 'break' your game, your game was very brittle in the first place.
That's basically my conclusion as well.
EDIT: based on my thoughts above, I'm going to give out an Immovable Rod in my next game, and before the players activate it I'm going to ask them if they think the Rod locks itsself to a fixed point in 3-dimensional space-time or if it locks itself relative to the nearest most powerful gravity well. I
REALLY hope they choose the former. *evil laugh*