You can enchant your arm like a weapon, but you have to arcane bond with it to cast spells through it. It weighs half as much for a small critter. Apply all rules of light or one handed weapons and unarmed fighting for its use. It does not count as a natural attack, as it is not natural to you. You can pick up anything that otherwise would not harm your mechanism, such as do not touch rust monsters or electricity. You can enchant it also with anything an arm or wrist or hand slot can be enchanted with, but these do not count as bonuses for the weapon's attack or damage unless you have the shield master feat. It may be directly targeted with called shots for all purposes as your arm and is also subject to any direct sunder attempts. You can not be disarmed of your arm.
I ran a 5e campaign with an enemy who had an electric prosthesis, but see rules, you could retrieve the golden plate from the corpse and cut off your own arm to use it, so I had to establish rules before hand.
I would rule a clockwork arm exactly the same as a Cybernetic Arm, except for appearance.
It's part of you, functions as a normal arm, and grants bonuses to things like climb and CMD vs disarm.
There are separate rules for attaching weapons to the arm.
I would assume that the weight of a clockwork prosthesis only applies when it is unattached (it is bizarre that arms and legs weigh the same in any event, but I would guess that the 'average' limb for a medium creature weighs about 25 lbs, so the replacement clockwork isn't any heavier.
The entry on it doesn't say it is in any way more limited than a normal arm, it only talks about things that it can do that a normal arm doesn't. There is though the enigmatic 'more specialized clockwork prostheses capable of...channeling magical energy' bit, which seems to imply that normal ones can't do that, but what exactly they mean by that is questionable. I would probably assume that the prosthesis could perform somatic components, but couldn't deliver touch spells.
The arm isn't a separate thing with its own hit points and hardness. Certainly something like burn, which triggers if you hit it with a sword will trigger if you hit it with your arm. Similarly a scarab of death will effect you, you are still holding it (just like someone holding it in a steel gauntlet is holding it). In certain circumstances a GM might give an advantage with something like a contact poison, but in general if something attacks you and hits, they hit you and you are effected by it (just like someone being attacked while wearing platemail over their arm would be).
I'm not really familiar with the called shot rules, but it is your arm, not a weapon, and should be treated the same. You can't sunder a creatures natural attacks (generally anyway) and your arm shouldn't be subject to sunder either
Change your name to 'Phillus Coulson Jr.' and get a SHIELD, alternativly you can go with 'Ashia Williams' and a chaisaw arm... they have chainsaws in PF Tech Guide. B^)
1: My character is a halfling and the prosthesis's weight is 25 lbs for a medium character. I saw two ways to calculate the new weight for a small character : either divide its weight by 2 like weapons and armor, or by 4 like clothing and containers. Which is appropriate in this case ?
Backpacks and clothes are surfaces.
Weapons are solids.Armor is screwy.
The arm is solid in nature. It should use the weapon's 1/2 weight multiplier.
2: Can a clockwork arm perform somatic spell components ?
Well, there is the Wizard Hook that is a hook hand that lets you do somatic components. I am sure the clockwork arm can do at least that.
3: Can a character with a clockwork arm safely manipulate objects or punch monsters that deal damage or apply a nasty condition when touched directly ( i.e. the burn universal monster ability, grabbing a red-hot steel bar, holding a scarab of death or other cursed item, a contact poison...) while the arm takes the hit as a separate entity ?
No. When you hit such creatures with a non reach weapon, you get the bad effect. However, you might be able to handle toxic substances with care. [For example, contact poisons.]
4: We use the called shots rule in our campaign, what makes losing a limb in combat possible, but are artificial limbs targetable with sunder combat maneuvers instead of called shots ?
No. It is a part of you. You cannot sunder it while it is attached. If it is carried, or unattended, then it can be sundered.
/cevah