Are my tax return's being held up and now overdue? Why are many labeled as "Rejected"? Do these have to be addressed?

Rejected means the IRS didn't accept the return to process.  So it wasn't filed.  Did you ever get an Accepted email?  Many of what says Rejected?  And if the federal return was Rejected then the state rejected too.

What is the filing status on your account?  When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc. What does it say?

Did you get a Reject error code or message?  A common reason is for the wrong 2024 AGI .

Try entering 0 for the AGI. The IRS might have processed your return later so the AGI didn't get entered in time.  Especially if you mailed it.  That works for most people. See,
https://ttlc.intuit.com/community/rejections/help/what-if-i-entered-the-correct-agi-and-i-m-still-getting-an-e-file-reject/00/27031

How to correct the AGI in the Online version
https://ttlc.intuit.com/community/agi/help/where-do-i-correct-my-agi-in-turbotax-online/00/26311

If you can’t get it to efile you will have to print and mail it.
https://ttlc.intuit.com/community/printing/help/how-do-i-print-and-mail-my-return-in-turbotax-online/00/26258

Be sure to attach copies of your W2s and any 1099s that have withholding on them.  You have to mail federal and state in separate envelopes because they go to different places.  Get a tracking number from the post office when you mail them for proof of filing.

Why are many labeled as "Rejected"?

Many of what are labeled rejected? Did you file many tax returns? Or do you mean that you tried to file the same tax return multiple times? You can only file one tax return with your name and Social Security number. If you filed more than one tax return with the same name and Social Security number, only one will be accepted. The others will be rejected as duplicates.

What is the reject code and message for the ones that were rejected?