All the article I can find seems to talk about multitasking and context switch as its a two different thing. It seems that multitasking and context switch are the same thing.
Yes, it is possible (depending upon what you mean by "context switch"). See cooperative multi-tasking. In cooperative multi-tasking, the operating system never needs to perform a context switch between tasks -- instead, tasks voluntarily take care of saving their own state and switching between themselves.
There are Superscalar and Vector Processors.
In order to truly multitask you have to be able to do multiple things at the same time. Normally this is done within human perception by context switching, it really only appears to do more than one thing at a time through, really its just like two people sharing a hammer and a bucket of nails, if they do it right, its like having two hammers and two nails as far as productivity, but to really multitask, you need more than one hammer or a hammer that can hit multiple nails at once.