The character should be moving at the speed of her current shape. You are fish, you move as a fish. On land, you don't move.
Otherwise, if you kept using the speed of the un-shaped character, underwater as a fish, you wouldn't move.
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The other relevant text from polymorph that wasn't quoted: "Your base speed changes to match that of the form you assume."
For other movement types though, you don't actually move at the speed of the animal you turn into. You move at the speed granted you by the spell you used. Beast shape 1 for instance gives you swim 30 if you turn into a fish, regardless of said fish's actual swim speed.
Also nothing prevents you from casting something like Carrying Wind to gain a fly speed and be a flying fish. Or Globe of tranquil water and swim anywhere you please (that spell is stupid broken. Jet through the sky as a giant squid, +8 to AC vs anyone outside the bubble because underwater combat rules, grab your foes from 30 feet away and drown them).
Crawling: You can crawl 5 feet as a move action. Crawling incurs attacks of opportunity from any attackers who threaten you at any point of your crawl. A crawling character is considered prone and must take a move action to stand up, provoking an attack of opportunity.
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Any creature with a speed of 5 feet or less can't take a 5-foot step, since moving even 5 feet requires a move action for such a slow creature.
So, you can move on land without a movement speed.
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So, you can move on land without a movement speed.Crawling: You can crawl 5 feet as a move action. Crawling incurs attacks of opportunity from any attackers who threaten you at any point of your crawl. A crawling character is considered prone and must take a move action to stand up, provoking an attack of opportunity.
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Any creature with a speed of 5 feet or less can't take a 5-foot step, since moving even 5 feet requires a move action for such a slow creature.I think those rules assume you have a land speed.
You might have been better off quoting the Special Movement Rules. Notably, its a Full-Round instead of a Move Action.Minimum Movement: Despite whatever penalties to movement you might have, you can take a full-round action to move 5 feet (1 square) in any direction, even diagonally. This rule doesn’t allow you to move through impassable terrain or to move when all movement is prohibited. Such movement provokes attacks of opportunity as normal (despite the distance covered, this move isn’t a 5-foot step).Or under Full Round Actions which talks about when you lack a sufficient speed. Again a full-round action.In some situations, your movement may be so hampered that you don’t have sufficient speed even to move 5 feet (a single square). In such a case, you may spend a full-round action to move 5 feet (1 square) in any direction, even diagonally. Even though this looks like a 5-foot step, it’s not, and thus it provokes attacks of opportunity normally.
Having a land speed of "-" isn't a penalty or a hampered speed. It is lacking the stat completely. If you lack a land speed you don't move on land.
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I guess you could use your Acrobatics Skill and move by Jumping. You would be literally a fish out of water flapping on the ground, presumably trying to get back in the water.
Creatures with a base land speed below 30 feet receive a –4 racial penalty on Acrobatics checks made to jump for every 10 feet of their speed below 30 feet. No jump can allow you to exceed your maximum movement for the round.
You would get a -12 to the check for having a base land speed that is 30' below the base value of 30.
The second phrase can be read as a continuation of the first where "land" was removed to reduce the world count (possible, as adding it would have pushed the text to the next row and the whole page is full of text) or it can mean that any form of movement is acceptable to determine the limit.Even with the second interpretation, with a -12 modifier and the DC doubled for the lack of a running start you are really moving like a fish out of water. ;-)
RAI, fish can jump while swimming, so I think any form of movement is acceptable to determine the limit, but you must be using that form of movement.
To return to the OP post, octopuses are aquatic creatures, so RAW, they breathe only water (even if in reality they can move a decent distance on land and survive for a relatively long time).
But the rules for breathing when Polymorphed have never been really addressed. If you become an elemental your new form has no ability to breathe normal air as your lungs are part of your original form. At the same time, they aren't an extraordinary or supernatural ability, so maybe they stay in place, but that generates some problem. You are breathing while moving as a blazing fire if you are a fire elemental?
Where are they when you take the form of a skeleton with undead anatomy I?
Decidedly confusing.
So, depending on the GM interpretation, the guy polymorphed in an octopus starts to suffocate as soon as he is on land or he can breathe air for an unlimited time.