As mentioned, there's some confusion here (and I've been using the restriction so long I forgot it's a house interpretation/rule).
The restriction is on Eye and real for that - and I believe it remains on the spells due to the fact in earlier editions each guideline had different base (in 5e it's all consolidated across). For Mentem it was Eye, where it started at 0 base. That's likely why most of the defined Mentem spells have Eye.
The House rule logic:
To target a mind (Mentem), similar restrictions as "you can't target what you can't see or have awareness of", or what can't be reached or "touched" by your Voice emanation. The mind can be thought of as hidden behind the person, so to reach it the magic must have a path - you have to use either R:Eye ("eyes are the path to the soul" kinda deal, but in this case mind), R:Voice - but unlike the Voice to reach anything physical in the world - there must be hearing to have a path to the mind (so this is not in the case when an element or Corpus is the target). I.e. Mentem via Voice does not work on the deaf or deafened.
R: Arcane connection will work as usual. Targets work as usual for Voice, but Eye is (optionally) limited to single target - so technically you could multi-cast them one-by-one, but not Eye an entire room or group in a single cast.
We've been playing with these restrictions to make the sagas more interesting and challenging, because honestly Mentem is still hugely overpowered, and it's such a get-out-of-problem and get-out-of-jail freecard when less restricted like in RAW. My players too much lean on Mentem to basically bruteforce too many things otherwise.
I'm also considering and using more dampening factors on Enslave the Mortal Mind and countering the ease of which opposition can otherwise be completely "data-dumped" and made to forget it ever happened with no-one the wiser. There's no more powerful magi than the Mentem specialist in the setting - it really is completely OP in RAW.
By the rules, Pilum of Fire doesn't need aiming. I suppose conceptually it is following your will, not your targeting. You could produce an aimed version, but it would just be worse.
Incantation of Lightning also doesn't need to be aimed, but does require a clear path to the target. It's weird that it has that rule and PoF does not. But magic is weird sometimes. Perhaps it's just a flaw in IoF.
No. The shooting at the person is just a cosmetic effect- it is actually created on the target and so is a direct effect. If it was otherwise, it'd have a rego requisite as creo itself cannot make a created flame shoot out.
(1) Add a basic restriction to magic: Hermetic magic cannot deprive a target of free will. So, for example, ReMe may be great at driving away ghosts, but it absolutely cannot control a human's mind.
(2) Any human who is not spiritually compromised (e.g. has no unconfessed sins) is immediately immune to magics that mess with their minds. So, the wicked may be subverted, but the virtuous may not.
Ah! I remember this one. The spell creates "an actual bolt of lightning" which is "highly unnatural" (starts from the magus's hand, rather than a cloud high up in the sky). Hence the clear path.
Pilum of Fire just creates a spear shaped fire, which "appears" to zap across, but actually just burns the target.
Haha, my players would hate me so much with those restrictions. I wouldn't go for 1) but I do have a lesser variant of 2). The virtuous to God do have some advantages.
I have another I use too, especially for the totql dominations like Enslave the Mortal Mind. Being enslaved like that means the target lose all own will and creativity - so the players will have to come up with very precise instructions and be very clear what they're asking for. Generic questioning doesn't quite work.
Additionally, Mentem masters and people trained in various mind techniques can hide things or slightly subvert or avoid specific planned for secrets (resulting in some ability vs ability rolls). Criamon can be a bit indecipherable.
Worth noting free will has a specific definition in Ars that is unintuitive- it isn't the capacity to choose but the capacity to choose between good and evil inclinations.
Human morality can be viewed as a
war between the inclination towards evil
that is a product of original sin, and the
inclination towards good, which is the
Divine gift of God. Jewish theologians
refer to these as the yezer ra and the yezer
tov respectively. Free will is the capacity
to choose between these two inclinations.
RoP Infernal pg 44
Thus Rego mentem isn't depriving one of their freewill- afterall, if a magus makes a person kill another person the former didn't choose that. No more than they did if someone took their hand and by force made them stab another. However, inclining a target towards sin may run up against such- that is, if the target is made to choose in such a way that that choice is forced.
Virtuousness would not change this, except insofar one might be so virtuous it is Essential or it may be a True Feeling.
Perhaps the clear path part was written with the Limit of Arcane Connections in mind? A magus cannot make something at a point they cannot perceive- then again it'd be odd if they added that for Incantation specifically...