Is it possible to use an iPhone without data?
This is most certainly possible. The first few months I had an iPhone, I didn’t have a data plan either.

In Belgium (where I live), iPhones are generally sold separately, without a data plan / SIM — they’re officially unlocked iPhones.

So, the answer to your question is: yes, it’s possible to use an iPhone without a data plan — but you can only change the SIM card if you own a SIM-unlocked iPhone.