What can you do with n iPhone if you don't pay for phone service?

Can you do everything else (connect to Wi-Fi, download apps, etc) except call/text and be able to access the internet? Does it basically just turn into an iPod Touch?

That is correct. However you need to be in a Wi-Fi location that offers wireless internet access such as Starbucks, McDonalds or through your home network. With Wi-Fi you will be able to access the internet, use your apps, download apps, email etc. You won't have a phone call plan plan or a text messaging plan through your cell phone carrier.

Use it like an ipod touch, correct.

Will I be able to text/video/call through applications like Google Duo or WhatsApp without carrier service on iPhone 4/4s?