Spell language states:
you create a phantasmal object, creature, or other visible phenomenon of your choice that is no larger than a 10-foot cube and that is perceivable only to the target for the duration. This spell has no effect on undead or constructs. The phantasm includes sound, temperature, and other stimuli, also evident only to the creature...While a target is affected by the spell, the target treats the phantasm as if it were real. The target rationalizes any illogical outcomes from interacting with the phantasm...An affected target is so convinced of the phantasm’s reality that it can even take damage from the illusion. A phantasm created to appear as a creature can attack the target. Similarly, a phantasm created to appear as fire, a pool of acid, or lava can burn the target. Each round on your turn, the phantasm can deal 1d6 psychic damage to the target if it is in the phantasm’s area or within 5 feet of the phantasm, provided that the illusion is of a creature or hazard that could logically deal damage, such as by attacking. The target perceives the damage as a type appropriate to the illusion.
So, let's say i create phantasmal red hot chains that come out of the ground, gripping each limb and dragging him down. If the target fails it's intelligence save, would it now be prone and taking 1d6 damage?
Disclaimer: All instances of real/reality used in this answer are with respect to the target thinking they're being affected. Phantasmal Force does not have the capability of actually creating something tangible, only to appear to be tangible to the afflicted target.
I've emphasized the important bit in the spell.
While a target is affected by the spell, the target treats the phantasm as if it were real.
Obviously this speaks to the reality of the spell.
A phantasm created to appear as a creature can attack the target. Similarly, a phantasm created to appear as fire, a pool of acid, or lava can burn the target.
That part details that whatever you describe can function as it normally would if it were real.
An affected target is so convinced of the phantasm’s reality that it can even take damage from the illusion.
And that part reinforces it all over again.
The phantasm includes sound, temperature, and other stimuli, also evident only to the creature.
That's the part where the illusion actually feels real to the affected target. This means that the chains, for all intents and purposes, are real to the target. Up to and including touch.
Obviously the writers couldn't outline literally every single illusion you can conceivably cast, so you have to extrapolate a bit. The three quoted parts above clearly demonstrate that the phantasm, for all intents and purposes, functions in whatever manner you describe as if it were real.
The balance is built in with the damage caused by the spell. It doesn't really hurt that bad at a meager 1d6, so using it as a means of crowd control is a far more effective and creative use.
So what can you do with this spell?
Well, you can't create things that are actually real, so you couldn't get a creature to cross a bridge no matter how hard it tried. It would simply keep falling and chalking it up to earthquakes or something.
However, in my opinion, if the creature is capable of performing the action without an external force acting on it, like being restrained by hot chains, then that is definitely within the bounds of the spell. It requires no contradiction and no actual force because the creature will act as if it is restrained.
This is reinforced by the last sentence of the spell:
The target perceives the damage as a type appropriate to the illusion.
This statement means, quite clearly, that the affected target is perceiving the pain of being afflicted by whatever illusion you cast. That, coupled with all the statements in the spell that treat the illusion as if it were real, and the stimuli accompanying the illusion, make it so that the illusion for all practical purposes, counts as real for the target, and the target alone.
The target rationalizes any illogical outcomes from interacting with the phantasm
The objects created by the phantasm are still illusions so they will not actually restrain/bind/grapple/whatever other status you want to use to hold them prone.
Say, for example, you created chains to bind the target. To the target these chains appear totally real, they can see them, they can feel the metal, they can see they are totally bound. But then the target tries to move. They strain mightily against their chains and.... their movement is totally unimpeded. The spell is still working so the target envisions it as bursting the chains, or the chains crumbling, or any other way as long as it matches up with the reality that they can in fact move. The chains are only an illusion so when the target tries to move.... they move. They wouldn't be taking damage unless there is a logical reason the chain could hurt them.
Another example would be a phantasmal flaming wall that appears over the prone target. The wall being made of fire is a good incentive for the target to stay prone and avoid being burnt. However they could choose to stand up if they wished and move through the wall. It would still cause them damage (1d6 as noted in the spell) either way.
For a final example let's say you created an illusionary creature to knock the target prone. When the creature tried to push the target the target would notice they are not actually knocked down. They would rationalize it and assume the creature missed, that they pushed the creature back, or some other way of explaining why it didn't work. They would continue taking damage as noted in the spell.
No, a character cannot be knocked prone or restrained by Phantasmal Force.
There is no text in the spell description that states the affected creature can be the subject of any mechanical conditions. What is stated is that it treats the illusion as real despite any contradiction, which will be rationalized away. Spells are restricted to doing exactly what they are described as being able to do.
Contradictions such as being able to see an ally through a wall are rationalized away. Being able to hear despite a fog horn blasting is rationalized away. Being able to move freely despite being engulfed by red hot chains is rationalized away. Being able to charge cage bars and pass through them is rationalized away.
Admittedly odd scenarios arise from this, such as a creature refusing to attack a real creature that it believes it can't see, while mechanically having vision of it. Rationalizing this contradiction is left as an exercise for the reader.