There is no RAW answer. It must be decided by the DM.
Firstly, this ambiguity is likely an intentional, direct consequence of 5e's design ethos of "rulings over rules" and the prominent role of the DM as the person that must make those rulings in the case where the rules are silent. Illusions and illusion magic are one area in which there is essential no general rules guidance, and thus falls squarely into the domain of DM-rule.
Jeremy Crawford said as much when asked about this exact question on Twitter:
Q: Can a creature under the effects of Phantasmal Force be restrained by it, i.e chains wrapping around a creature?
A: Phantasmal force details the few game effects that it can reliably create. A DM is free to allow additional effects.
Because illusions are a complicated issue, I will outline two of the major DM approaches to this issue. Since they take opposite stances to each other, any DM reading this will have to figure out which way makes the most sense, seems the most fun. and/or which way aligns better with how they've already been handling it.
The core of the disagreement is whether the DM rules that an illusion fools the mind so thoroughly that the body will react physically to it or not.
Interpretation 1: No, Phantasmal Force cannot chain someone and force them prone
In this argument, the spell looks and feels like a chain, but the chains (not being real chains) would not be able to restrain the creature since they would offer no resistance when the creature tries to struggle out of them.
The target rationalizes any illogical outcomes from interacting with the phantasm
Because of the above effect from the spell, the mind of the creature would try to rationalize this in some way (the chains broke, the chains loosened temporarily, etc.) but they would still believe the illusion to be true.
In this way the creature would not gain the prone condition because their movement is not actually inhibited in any way even though they believe the illusion is real.
See this answer for a more thorough take on this interpretation.
Interpretation 2: Yes, Phantasmal Force can chain someone and force them prone
In this interpretation, the chains really do restrain the creature because the creature treats the chains as real chains, even though they are not.
While a target is affected by the spell, the target treats the phantasm as if it were real.
The chains also sound and feel real to the target in every way.
An affected target is so convinced of the phantasm’s reality that it can even take damage from the illusion.
So, in this case, when the creature tries to escape from its restraints, its mind, thoroughly convinced that the chains are real, will act under that assumption. Thus, the creature's limbs will be bound. And this creates the case for the fact that the creature is able to gain the restrained condition from this spell.
See this answer for a more thorough take on this interpretation.
Decide but stay consistent
So I have provided very brief overviews of two interpretations of the spell's effect. There are certainly more of them out there. As a DM, the key is to decide on one and apply it fairly, transparently, and consistently. Not only across this spell but other similar ones.
Yes
On a failed save, 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. (Emphasis mine)
A body-shaped mass of lava definitely counts as a 'visible phenomenon' (which is almost an all-encompassing term anyway). The character can certainly fit inside a '10-foot cube', so that requirement is met. If you were unsure as to whether the illusion could occupy space already taken up by the caster themselves, then they could simply create an illusion of a lava body covering, just outside the skin, bypassing that problem.
The player could even argue that the d6 damage per round could be perceived as lava flying from their body, and onto the creature, although you may want to disallow that.
Best Answer
Yes, it can heal the target. (Qualified)
There are a variety of healing (as in hit point recovery) mechanisms in the PHB that do not require (a) some sort of medical knowledge/skill, or (b) magic, including spending hit dice during a short rest, hit point recovery during a long rest, temporary hit points accruing to a character and/or her allies as a result of (non-magical) class features. Indeed, in the real world, the field of psychosomatic medicine is concerned with precisely the question of how one's beliefs, perceptions, emotions and state of mind influence health and healing (e.g., placebo effects are one such example).
Therefore it is reasonable to infer that phantasmal force can cause healing (temporary or permanent). Of course, 5th ed. D&D is predicated on rules in the broad stroke, with DM fiat, rulings or house rules on the details (for example, such healing might be ruled to require the availability and expenditure of hit dice, etc.), so of course "it's up to the DM."
One might argue that the psychic damage mechanic described in the write up for phantasmal force somehow indicate only a possibility of psychic harm. I disagree that there is no mechanism for healing (see my first paragraph) given the spell description's emphasis on effects on the beliefs of the target creature.