I’m extremely sorry you ran into this issue. The problem lies with the the mirrorservice.org mirror which has been blacklisted by us for some time. Unfortunately MyEclipse 8.0 included an older version of Pulse which did not have the blacklisting rule set. Simply leaving the dialog open (ignore it) will not cause more to pop up while other downloads should continue from other mirrors, towards the end of the process, you can cancel this dialog.
Due to the load on our servers due to the fresh 8.5 release, some update operations may take longer than usual, though you should never have had to force quit the application.
For others who run into issues with the 8.5 update, please see this note: https://www.genuitec.com/forums/topic/issues-updating-to-myeclipse-8-5/
I can understand your frustration with the update process and regret the inconvenience caused. 8.5 includes Pulse 3.0, a significant change from Pulse 2.5 which should prevent issues like this from recurring in the future.