step up, following step and difficult terrain

[P=NP?]

can step up {core p135}, Following step {APG p160} or step up and strike {APG p170}

be used in difficult terrain or when movement is hampered? why or why not?

[Syries]

Moving in difficult terrain means moving one square costs 10 ft of movement and step up uses the 5ft step action. Following step doesn’t change the action type (5ft step) despite allowing you to move 10 ft,, and a 5ft Step is explicitly forbidden in difficult terrain unless you have a feat or ability like Nimble Moves.

However, it’s a different case if your movement speed is hampered as opposed to terrain costing double movement. If you’re under the effects of the Slow spell, your speed is halved, but moving 5 ft is still just moving 5 ft, meaning you can still take a 5ft step (and thus, you are able to use step up, following step and step up and strike)

[blahpers]

Pretty much. Relevant quote:

Core Rulebook wrote:

You can only take a 5-foot-step if your movement isn’t hampered by difficult terrain or darkness. 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.

[Cavall]

I would personally let someone who could take a 10 foot "5 foot" step to take 5 in difficult terrain.

But that's a bend to honest. Not one I think beyond the scope of imagination but yeah by the strictest reading it can't be done.

To be honest I can't imagine a single developer who would say no to that idea.

Regardless there is a feat that allows 5 foot steps so at least theres a way out.