Does it cost money to send or receive a text from someone in another country if they have a U.S. number?
Yes, international texting costs extra. One way around it is to use Skype or something comparable. See details at http://phones.verizonwireless.com/skypemobile/
If the recipient has a US. number there will not be a extra cost involved for sending or receiving text messages while they are out of the US.