At the end of Episode 1, Danny is shown strapped to a bed with his sleeve rolled up and an IV inserted in his right arm. At the beginning of the second episode, the sleeve is rolled down and underneath the wrist restraint.
During the conversation between Ward and Joy in her office, Joy<s cup changes position depending on the coverage. On hers, Joy hold the cup by the handle. On Ward's coverage, she holds her cup by the body, with the handle away from her.
Danny Rand is placed in what is referred to as a "72 hour psychiatric hold." Since the Meacham's are not his relatives and the narrative clearly states that law enforcement was not involved, this would not be possible.
Failing an arrest report and/or a visitation with a psychiatric expert appointed by the court, there would be no LEGAL method to do this. Any ILLEGAL methods would result in the Meacham's arrest and possible prosecution as well as the psychiatrist and possibly the facility losing his/its licensing.
During Ward and Harold's phone conversation, both can be clearly seen holding their phones to their ears with the screen still illuminated. However, most, if not all smartphones have a sensor that deactivates the screen as it gets near to your ear to prevent accidental button pushes.
Colleen would not be allowed to just walk around the city with a sword strapped to her back, real or otherwise. It would be considered a dangerous weapon and she would have been arrested or it would have been confiscated, at the very least.