I have recently created a psychic with psychic duelist archetype and i was talking to my friend and she mentioned that since it was a mindscape one could manifest a cake and eat it without gaining any weight. What i want to ask is whether it is actually possible to manifest non-combat related manifestations in a psychic duel.
You cannot manifest non-combat stuff in a psychic duel
A binary mindscape is typically only a minimalist backdrop for a psychic battle—a ghostly image, like a stark memory, lacking detail and verisimilitude. It might manifest as a flat surface surrounded by fog or a featureless plain of grass on a cloudy day. Sometimes, a binary mindscape mimics a real-world locale the creator knows well, but even then, the details at the edges of vision are usually fuzzy and indistinct, and features that invoke lesser senses, such as smell and taste, are lacking. A binary mindscape has no effect on the psychic battle; it’s merely a mental construct used to assist the participants in visualizing their actions.
And neither of you have full control of it.
Once within the mindscape, a creature can expend psychic energy to create mental hazards called manifestations to damage the other combatant or to reshape the mental landscape. Because the mindscape becomes a shared mental space after its creation, neither participant in the battle truly controls it, and they both have an equal ability to alter the environment once their minds are connected.
Binary mindscapes are far more limited than Immersive mindscapes (which your friend is probably thinking about), things are not real and everything you see is a psychic manifestation of both brains working to defeat each other. So creating a cake on a binary mindscape wouldn't have any taste or smell, but that doesn't mean you can't create cakes.
The main difference between the two mindscapes types is exactly your physical senses. In a binary mindscape your mind is within the mindscape, but your body is still active in the real world, and everything that happens to it can be felt, including damage and healing, which may hinder or help you in the duel. While in an immersive mindscape, your mind is completely disconnected from your body, replacing the body’s actual sensory perceptions. As such, all sensations are vivid and feel real, and you can't feel anything that happens to your body, because your mind is immersed in that new reality, just like in a vivid dream.
Otherwise, the limit is your imagination
Combatants creating psychic manifestations are limited only by their imaginations as to the look, sound, feel, and smell of each manifestation; these sensory effects guide combatants in their later choices.
Since you are normally limited to either attacking, defending or creating a thought-form creature during a duel, that cake she mentioned must either be a form of attacking or a thought-form creature (which might attempt to run away to escape being eaten).
Psychic mindscapes are, otherwise, limitless. You can think about it as a dream where the creator has complete control of how it looks, smells, feels like, and how others will perceive things in there. The rules in a duel are limited because the objective in there is to defeat your opponent, not get them diabetes. If in the middle of a combat, you decide to take out a cake and eat, that's on you and your opponent is probably going to take advantage of that.
In an Immersive mindscape, it really doesn't matter if you create a cake in a mindscape and eat it, it will feel like a cake and taste like one, if you ever ate one that is. You probably couldn't imagine an atomic bomb specifically, as your character couldn't possibly imagine something he never read, heard or seen before (and even that is arguable). But you could imagine a bomb that explodes in a vast area destroying everything, which is perfectly reasonable.
And even this has exceptions, you could obtain a glimpse of things you never seen before by accessing the Akashic Records, the extraplanar repository of all experiences that have ever occurred everywhere. Knowing for a fact that our planet exists within Golarion's setting (in a far, far galaxy), events that happened in the real world could be seen in the Records.