Yes this is correct. For the second question, in the context of applying the Teamwork keyword, no.
For reference:
[Old] Teamwatch: When a character with Teamwatch is active and you field another character die with the same affiliation, use their Teamwatch ability.
[Revised] Teamwatch: When a character with Teamwatch is active and you field a different Character die with the same affiliation, use their Teamwatch ability.
Under the old definition of Teamwatch, there was confusion on what the word “another” meant in this context, since it can have two definitions. The first can mean ‘more of the same’, e.g. he had
another slice of pizza. The second can mean something different, e.g. she came to the party with
another man.
To clear-up this confusion and clarify the intent of this ability, the revised definition of Teamwatch changed “another” to “different”, which encompasses the second definition above. The fielding of an identical character die will not initiate a Teamwatch ability. Therefore, Teamwatch can also be explicitly stated as:
“When a character with Teamwatch is active and you field a
Character die that is different from the Character with Teamwatch with the same affiliation, use their Teamwatch ability.”