Dynamo can only do what Revit can do - that is if you can’t do it in Revit then you can’t do it in Dynamo.
There are however some good work around for just about any intended result though so knowing a bit more specifically what your after might help.
There is likely a better way to accomplish your end result, but my knee jerk reaction is yes to both but not natively in the manor you likely want. I would look into alternate work flows or
Since revit can’t combine a material takeoff schedule with a multi category schedule the short answer is no.
You can however write the parameter values to new parameters set up in a multi category schedule.
Again since there is no way for to reuse a schedule to filter by tag value is in use in a particular view, the short answer is no.
You can however set up a new yes/no parameter ‘OnSheet#*’ for each sheet you want the schedule on, and use Dynamo to read every material tag in every view ok the sheet in question and mark the parameter yes/no accordingly. Then duplicate the schedule and place on the respective sheets filtering by the sheet number.
If this sounds convoluted or elaborate it’s because it is. You’re asking a program to break the rules of a program it’s driving, and that’s generally a bad idea.