It's beginning to get difficult to keep all our comments in a single reply; I'm going to try just starting a reply from scratch and including quotes if/when necessary.
Important note: When Quicken sees a security in a download that Quicken does not recognize, Quicken presents the user with a dialog that has two options ... the user must chose one of the two options. Making the wrong choice can create the type of problem you are experiencing.
1.) Is this a new security? If the user answers yes, a new security will be added to the Quicken Security List and the downloaded transaction containing that security (and any subsequent downloaded transactions for that security) will contain the name of that security. When the new security is added to the Security List, it is given the Ticker Symbol found in the downlad and assigned the CUSIP number found in the download.
2.) Is this security the same as an existing Quicken security? If the user answers yes, the downloaded security will be given the same characteristics as the existing Quicken security, including name, ticker, and CUSIP number.
I think your problems likely all result from you having answered those questions incorrectly; in some cases creating a new security when the downloaded security was really already in your Security List, in other cases matching the downloaded security to the wrong existing Quicken security, or even treating a downloaded security as a match to an existing security when it should have been treated as a new security.
For your securities that have the wrong CUSIP#, that's probably because you matched the downloaded security to the wrong existing Quicken security, or failed to create a new security. For your securities that have no CUSIP#, those securities have not been matched to any downloaded security.
I think you have two possible approaches to repair the damage:
1.) Reprocess the problem securities in your existing file.
That means un-matching all the securities that are involved (and that indicate they are "matched to an online security"), then going to Tools > Online Center, selecting the appropriate financial institution and account, opening the "Holdings" tab, and clicking "Compare to Portfolio". That should present you with the same two "options" I mentioned above for each downloaded security which Quicken does not recognize - giving you the opportunity to correctly create new securities or match existing securities.
[To "un-match" a security; select the security in the Security List, click the Edit button, and remove the check mark from the "Matched with online security" box. If you created a new security when you should not have, it may be necessary to delete that unwanted new security.]
2.) Restore a backup from just before the problem download, and download again. This should give you the same options mentioned above for each downloaded security that Quicken does not recognize. This would likely be the most straightforward approach.
"I have written down both CUSIPs. How can I add them?"
You don't add them yourself; Quicken assigns them as part of the process of identifying downloaded securities - as noted above.
"Online Center? Where is that?"
Tools > Online Center
"Is a possible solution to all, or at least some, of these to delete the securities I no longer own from the security list?"
NO!