Will I receive text messages once I turn off Do not Disturb on my iPhone?

Where will they appear?

No you won't, but when you go to the main screen there will be a red number on top of the message icon

You still receive text messages with Do Not Disturb on, you just don't get a notification telling you that you just got a text. Simply open up your messages app, if you don't have a new text then nobody texted you

Nope. They will be pushed to you once you disable "do not disturb".

DND doesn't stop texts from coming, just stops you from being alerted of them

You will get texts, calls, etc. They will show in the screen (if you have enabled this) but your phone won't buzz, ring or notify in any way. The screen won't even light up. Hence "Do not disturb"