Should we move to Oslo?

Hello!
My husband has an opportunity to relocate with his company to Oslo. We are not at all familiar with Norway and don't want to pass up a good opportunity. Here are some concerns we have after some research. If anyone could clarify, comment or advise we would really appreciate it.

Cost of living:
I understand Norway is a wealthy country overall. If we are not, will we have a hard time getting by? We have two month old daughter.

If I am an American expat staying home with our daughter, will I have a hard time meeting other folks who are in a modest financial situation as well?

Taxes? We passed up the opportunity to go to Zurich because the taxes would have left us broke. Any surprises for us in store there as we consider this move?

Safety:
We've read about a rise in crime in Oslo, specifically the eastern part of the city. Is this accurate? How does the safety compare to say, London, or New York City,
where we live now?
Can we find affordable housing outside of the "unsafe" neighborhoods?

Childcare:
Any info would be helpful, in case I need to return to work.