a) Do you think it’s rude not to respond to a text message?

Someone has to stop talking first! Like Divine said, not all messages require a response. Expecting an immediate response from someone is rude.

b) Do you think it’s rude if people text you but rarely or never have time for a phone conversation with you?

No, that seems normal to me, maybe because I'd rather text or talk in person than talk on the phone.

c) Do you think it’s rude if people want to talk by text but never invite you to do anything while they have groups of friends they often get together with?

I don't know if I would call it rude, but it stings. It's a sign they aren't invested in a friendship.

I enjoy texting, but I have friends and relatives who just don't do it. It would be obnoxious for me to keep texting those people even after they've told me it's not a medium they enjoy, much ruder than it is for them to not reply to my messages.