Hey all, I have a few questions regarding special objects.

Both Ghost-Spider and Spider-Man 2099 have the Dimensional Travel Watch trait that allows them to start with the #s003 Dimensional Watch equipped at no cost. Could I have both of them equipped or does it conflict with the special objects rule?

From my understanding, the #s003 Dimensional Watch does not count towards my 3 objects during force construction and I do not have to pay 5 points for it due to the trait. My opponent still scores the 5 points if my Ghost-Spider gets KO'ed right?

Thank you!

IIRC, yes. IIRC Special Objects that a character starts the game with are considered to have come outside of the game, so they would not conflict with the force construction rules.
BTW please remember that special object are considered Unique (so without this trait you would not be able to have tow watches on the force)

When a player KO a game element that has a point value they score the points. Regardless of whenever the other player paid the point value or nor.
So for example summoned charaters like Suited Henchman.

Correct, the Dimensional Watch is considered to come from outside the game.
Your opponent would have to use a destroy action or pick it up and use it in an object attack or TK the object and attack with it, to score the 5 points. Also, your opponent could equip the Dimensional Watch to one of their characters, since it is EQUIP: ANY. They would not score points for it, but, it would grant them the effect.