a) Technology may or may not make us more productive, it depends on what you mean by productive and what the situation is. If the situation is school or school work then no, it is more of a distraction. But if you're referring to an office job then yes it helps us a lot. For example: a student is supposed to be doing phsycology but instead he/she is playing with their phone which doesn't help us learn at all.
b) "Multi-tasking"/"task-switching" has a lot of consequences. The most common consequence that most people know about are developed by driving and doing something else, like talking on the phone or even drinking. To drive and think that you are able to text or drink at the same time is not the proper thing to do, it normally ends in a car accident because a person who is text messaging and driving looks away from the road for 4.3 seconds at a time on average. Multi-tasking also shrinks the human brain causing memory loss and stress. When people multi-task it usually ends up that they do a sloppy job at one of the tasks.
c) Our elders are correct, young people now-adays don't know a lot in-depth because we have access to the Internet which doesn't cause us to think as much as human kind used to. But the evolution of human and technology relationship is always changing, so in theory we are not getting dumber, we are getting smarter, just most of our learning skills are directed toward the use of technology.
