I’m on my parents phone plan, and we don’t know if twitter tweets are included in our package for texting. I have verizon if that helps, and I have the NV2. How do I figure out if tweets are included or cost extra?

If i wanted to get twitter on my cell phone from verizon wireless do i have to have internet or do u like text twitter like how does that work and do u have to pay extra and how can i find out how much?

p.s. i have unlimted texting
i live in the us