A wizard has a familiar and some other minions. Let's go with a summoned monster and a non-intelligent undead minion. Can the familiar give commands to these other minions?
Does it matter if the wizard is present? (Like if they get teleported away) Does it matter if the wizard is conscious? Does it matter if the familiar can speak? Does it matter if how the wizard is controlling the undead (create undead vs command undead)?
Any other edge cases one can think of?
tl;dr
It depends, but probably - at least much of the time.
Summons
Both Summon Monster and Summon Nature's Ally include the provision:
If you can communicate with the creature, you can direct it not to attack, to attack particular enemies, or to perform other actions.
Presumably, "other actions" could include a command to "obey my familiar". Check with your GM first, but this GM has no concerns about giving such an instruction to a summoned creature - especially an intelligent (INT 3+), summoned creature.
In this case, both the wizard and the familiar would need to be able to speak to the summoned creature.
Undead
Create Undead explicitly doesn't grant any control over the created creatures ("Created undead are not automatically under the control of their animator."). However, it does offer the ability to use Command Undead (and, potentially, Control Undead: the wording's a bit unclear) as part of the creation process.
Command Undead is basically "Control Undead, but longer-lasting", and Control Undead offers:
You command them by voice and they understand you, no matter what language you speak. Even if vocal communication is impossible, the controlled undead do not attack you.
Control Undead can also clearly be used on intelligent undead - the spell description mentions that such "creatures remember that you controlled them, and they may seek revenge".
As with summons, it seems entirely reasonable that the caster can command undead (especially intelligent undead) to "do what my familiar tells you to do". However, Control Undead would not extend the "no matter what language you speak" benefit to your familiar; the familiar would need some way to talk to the undead in question.
Hirelings, cohorts, and the like
Of course, any creature you're paying or have otherwise convinced to follow you on your adventures could probably be instructed to follow the familiar's instructions just like they could be instructed to follow the instructions of another party member (or even an NPC - nothing's stopping PCs from having their cohort guard the mayor for a few days while they're looking for the person sending threatening letters).
Dominate
Both Dominate Person and Dominate Monster (which is "Dominate Person, but without the type limits) allow telepathic control:
You can control the actions of any humanoid creature through a telepathic link that you establish with the subject’s mind.
They also include the provision that
If you and the subject have a common language, you can generally force the subject to perform as you desire, within the limits of its abilities.
I see nothing that would allow a wizard to transfer the telepathic bond to their familiar. However, again, "follow my familiar's orders" seems to be entirely within "the limits of [the] abilities" of an intelligent creature that's been dominated.
Charm
Charm Person (and the handful of spells that are "Charm Person, but with different type limits") says:
The spell does not enable you to control the charmed person as if it were an automaton, but it perceives your words and actions in the most favorable way. You can try to give the subject orders, but you must win an opposed Charisma check to convince it to do anything it wouldn’t ordinarily do.
It also says that:
You must speak the person’s language to communicate your commands, or else be good at pantomiming.
Again, while I find nothing that would inherently allow a familiar to be treated as the "you" in the Charm spells, "here's my familiar buddy; please listen to their suggestions" would most likely be a reasonable request. However, the "you" in "you can try to give the subject orders" does seem to be fixed to the caster and not their familiar.
A caveat here: the Charm spells do specify that the target "regard[s] you as its trusted friend and ally" (emphasis mine); if they would be unlikely to let an animal of the familiar's kind hang around them normally (eg., afraid of snakes and the familiar's a snake), the caster would need to use the "orders" clause.
Familiars
The long-form description of Familiars doesn't give any indication that a familiar's abilities are adversely affected by the state or location of their master, with a couple of exceptions (Empathic Link has a 1-mile range, and Deliver Touch Spells requires the master be touching the familiar to cast the spell).
And, it's not even entirely clear that the familiar loses any of its abilities if its master dies. FWIW, this GM would probably have the familiar leave the party unless there was a good chance the master was going to be resurrected soon (though I could see a familiar staying in the game, watching over their old master's wizard school or something).
Summary
In summary, it appears to this GM that authority can be delegated to a familiar exactly as it could be delegated to another party member. The Charm spells are probably the hardest to delegate, but they seem to be written to make control hard (ie., that seems to be a feature, not a bug).
