Text messages? Email messages?
To the hard drive? On your computer?
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
That was 4 questions Ann154 asked you, with only 1 response of "yes". Was that a yes to ALL 4 questions?
As to the emails, simply access the emails from your computer and save them from there.
As to the text messages, you can either forward them as emails to your email client and save them from your computer or you can install a texting backup app such as SMS Backup & Restore on your phone and back-up the texts. You can then send the backup file to your computer, either via email or a file explorer such as ES File Explorer installed on your phone, to save on your hard drive.
If you install Verizon Messages on your phone, you would be able to access any future texts directly from your computer from within your MyVerizon account.