If we consider a deponent verb such as arbitrārī in the perfect tense, hence arbitrātus sum/es/est, is the participle arbitrātus supposed to be declined like a regular adjective? For example if one wants to say
Syra thought that Quintus was dead
is it
Syra Quintum mortuum esse arbitrātus est
or
Syra Quintum mortuum esse arbitrāta est
?
It is the second option with arbitrata. For the purposes of agreement, you can think of the participle as an adjective, so that Syra arbitrata est and Syra Romana est have exactly the same form.
The gender agreement holds for all subjects of all numbers in the same way. For example, uxores arbitratae sunt and mariti arbitrati sunt. And there is no difference between passive perfect forms of normal transitive verbs and active perfect forms of deponent verbs. Deponent verbs are not special in any way here.
