I assume you are referring to combat manoeuvres that can be attempted in place of a melee attack, namely trip, disarm, and sunder.
According to this FAQ on the Paizo website:
When making a trip combat maneuver, you don't have to use a weapon with the trip special feature--you can use any weapon. For example, you can trip with a longsword or an unarmed strike, even though those weapons don't have the trip special feature.
Note that there is an advantage to using a weapon with the trip special feature (a.k.a. a "trip weapon") when making a trip combat maneuver: if your trip attack fails by 10 or more, you can drop the trip weapon instead of being knocked prone.
On a related note, you don't have to use a weapon with the disarm special feature (a.k.a. a "disarm weapon") when making a disarm combat maneuver--you can use any weapon.
From this answer, it seems clear than an unarmed strike is considered a weapon that can be used for combat manoeuvres.
Sundering with a normal unarmed strike is not possible because because objects are immune to nonlethal damage. See Smashing an Object on this page.
Note, however, that an unarmed character does not threaten nearby spaces, so an unarmed character would not be able to make combat manoeuvres such as trip as an attack of opportunity. "If you're unarmed, you don't normally threaten any squares and thus can't make attacks of opportunity." See Threatened Squares under Attacks of Opportunity in the combat rules.
Yes, subject to all the relevant restrictions (like provoking an attack of opportunity). Why do you think they can't be? In fact many combat maneuvers (e.g. bull rush) don't really make use of a weapon at all.
Naturally there are specific exception rules, like for disarms "Attempting to disarm a foe while unarmed imposes a –4 penalty on the attack." These are all contained in the combat maneuver descriptions themselves.