This Webquest should take probably 2-3 periods to complete depending on whether or not the required reading (Acts 1 and 2) are read in class or assigned as homework. If it is, then the research and the group work for the dating profile should be done in 1-2 classes (depending on how well the students stay on task and are able to work as a group. I would suggest creating groups beforehand to avoid possible disruptions, but that is up to the discretion of the teacher. After that, it should take just one additional class to complete the presentations as they will likely last no longer than 5-10 minutes.
In case of equipment difficulties, you might provide students with a detailed summary of the play in case online research is not easy to complete. This way students will be able to better understand the play before analyzing each character but they are not restricted by lack of internet access.