No, I am afraid under the best evidence rule a sworn affidavit would not substitute for a deposition. An affidavit can be submitted with pleadings in the court case, but they are considered hearsay in court and not evidence unless you have the party who swore to the affidavit physically appear to testify. The reason for this is a deposition is taken under oath and the opposing party is there and has a chance to question the person, whereas an affidavit is drafted and signed without any change to cross examine the person giving it.
You can walk into any court in the Dallas Court building and you can usually ask the clerk of court and they can tell you which courts have civil trials scheduled for you to sit in on and view.
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