can we associate a file against to several team areas in RTC according to a customized field?

Jane,

one important point in development is and has always been responsibility. You want to be able to have a clear responsibility, because, as we have learned, if you have multiple or ambiguous responsibilities you don't have responsibilities at all. This is the reason why there is a identifying 1:1 relationship between categories and a process area and also for just one work item owner.

The categories are designed to be human readable so that users can choose a reasonable one and to allow teams to see their work.

So, the category in RTC can only map to exactly one process area (team area or project area). You can not change that at all and it is as it is. Using subcategories to manage this is one way of doing it. If your managers disagree with that, well is rejecting reality.

If teams work together on a feature, there should be a work item for each team to track their work and for planning.

I am not a fan of using calculated values for this. You could likely do that, but it will be a nightmare to maintain the mapping. I am not sure how to help you with your problem of the impact of all these changes. The problem, I think is rather the management and not the tools.

One other thought would be to make filed against optional when the users file them and have an attribute for the feature and then the team leads file the work items to the categories they think match their structure best.