Arcane connections are established by a variety of means, be it emotional attachment or physical attachment or similar. There is a list of the kind of things that can be arcane connections on p84 of the core rulebook, in the box labelled 'Arcane Connections'. As you can see on that table, Fury's wooden knife would indeed be an arcane connection were you able to get your hands on it, but a lock of his hair would be a more effective arcane connection.
Magi don't create arcane connections, they find them. The easiest way to get an arcane connection in the field is to steal something belonging to the target or to take a chunk out of them. For example, if a grog manages to wound a beast with his sword then the blood on his sword is an arcane connection to the beast.
What a magus can do is fix an arcane connection. This is a seasonal activity that involves taking an existing arcane connection and msytically preserving the bond it has to the target. Thus, if you took Fury's wooden knife and spent a season fixing it as a connection, the result would be a mystically stronger connection than a lock of his hair or a pint of his blood.
Penetration multipliers for arcane connections (and sympathetic connections) are purely about overcoming magic resistance. If the target doesn't have magic resistance, none of this matters.
No, not every spell. Magic resistance applies if any of the following are true at the moment the magic resistant target is affected:
- the spell directly targets the creature with magic resistance (e.g. an Intellego spell to look through someone's eyes)
- the spell creates something magically that then affects the target creature (e.g. Pilum of Fire)
- the spell modifies or controls something that then affects the target creature (e.g. The Crystal Dart)
It is worth noting that any spell you can effectively cast via an arcane connection will be resisted. You can't cast 'Pit of Gaping Earth' at the feet of someone to whom you have an arcane connection unless you can see / have an arcane connection to the ground he's standing on. Pit of Gaping Earth doesn't target people, it targets ground.
If the spell range is 'sight' then the target must be close enough that the caster could see them if no obstructions were in the way. In addition, the caster must be able to sense the target OR must have an arcane connection. So if, for example, you have an arcane connection to a guy who is on the other side of a wall, you can target him just fine.
If the spell range is 'eye' then you must have an unobstructed view of the targets eyes and they must be looking into your eyes. Both of you must be able to see the other. This is intentionally very restricting; it's designed for 'look into my eyes...' spells, and is typically useless for combat.
To go back to your original post...
A spell of range 'Arcane Connection', such as 'The Inexorable Search' could be used to locate the covenant member. As long as the spell has a range of 'Arcane Connection' it'll work just like any other spell. Assuming the covenant member does not have magic resistance, none of the multiplier stuff matters.
In this case the Magus is out of luck. In your example, all he knows are the name of the magus and what he looks like. While these can be used to create sympathetic connections, neither of these are arcane connections. No arcane connection means no spell targeting.
Now, if the magus has also got an arcane connection (a lock of hair), then...
A lock of hair has a penetration multiplier value of +3.
The magus also knows the name of the target, which is a sympathetic connection of +1.
The magus also knows what the target looks like, so if he creates a symbolic reference such as a small doll then that's another +2.
This gives a total penetration multiplier bonus of +6. We add this to the default penetration multiplier (1) for a penetration multiplier of 7.
The caster now attempts to cast the spell. Lets assume, for argument's sake, that he manages a casting total 2 points lower than the spell level. This means the spell goes off, the magus loses a fatigue level and the penetration total is currently -2 (casting total - spell level = -2).
Lets assume that the target has a relevant form score of 5 and is standing in a +2 magic aura, so his magic resistance is 17.
Now, lets assume the caster has a penetration ability score of 3. The final penetration bonus is penetration ability x penetration multiplier. The default penetration multiplier is 1, but because of our penetration multiplier bonus, the final multiplier is 7 (1 + 6 = 7, as calculated earlier).
This means the penetration bonus is 3 (ability) x 7 (multiplier) = 21.
We add this to the current penetration total (-2), for a final penetration total of 19 (-2 + 21 = 19).
Because 19 is more than 17 the spell successfully penetrates and takes effect. The caster is now able to see through the eyes of the target.
If the magus did not successfully make a symbolic reference, his penetration multiplier would be 5. This would mean his final penetration would be 13 (-2 + (3x5)), which would not be sufficient to overcome the target's magic resistance and the spell would fail.
All of this assumes the spell being cast is of range: Arcane Connection. If it isn't, it's not going to work because the target is out of range.