The final battle

[Future Esthar]

2)I believe she is possessed by Ultimecia yet in the second disc.Better,I believe that she is Ultimecia.
But to answer your question:Ultimecia is using Junction Machine Ellone.So she can use some sort of cassete tape to send its content through junction.Maybe she record a speech in the tape and put it on the machine to send.Maybe the machine receives visual signs from Squall´s era.So it is not implied that she uses it directly on her head.
Concerning your question about Adel.Ultimecia was herself possessed by someone on the future(relative to Squall´s time).So I use the word "Ultimecia" to sustitute the name of this powerful being.The person who uses the cassete tape is not the "Ultimecia" from the game but a more powerful being.And I didn´t said Ultimecia was Adel but True Ultimecia is (Ultimecia Transforms into Adel).