Can I use iphone 5c without SIM card?

So I'm going on a cruise soon and I need to take out my SIM card from my iphone so I don't use internet, because it will cost more to use internet out of the country. So i was wondering if I could still be able to take pictures with my phone without the SIM card in it. And if I put the SIM card back into my phone, will the pictures I took still be on there? And I also heard if you turn on airplane mode, your phone won't use internet… Could I do that in the cruise instead?

Yes, you could use Airplane Mode instead. Would achieve the same result, could use Wi-Fi though. Wouldn't be an issue.

But to answer your questions anyway, yes you could still use the camera without the SIM & removing it has no effect on if they would be there or not since that is stored in the phone's memory & SIM cards are not memory cards.