Deleting from webmail also deletes from email client? Really? How much worse could Cox webmail be?

I can't send emails from my Mac mail. When I try, I get the following message:

The SMTP connection to server “smtp.cox.net” failed.

Select a different outgoing mail server from the list below or click Try Later to leave the message in your Outbox until it can be sent.

The issue started happening a couple of weeks ago; it may have coincided with a Cox outage. In any case, I did not change any settings. The settings are identical to those on my other computer, where I have no problems sending emails. The only difference is that this computer has a newer OS. I have started to research this and have found people with similar problems but no solution yet; haven't had the time to do further research myself and I can't go through the motions with the cox technical support to confirm that yes, my settings are correct and it must just be a mac issue. I know there are mac issues, including that infuriating inability to push emails so you have to check for them. I am so sick of coping with one email problem after another that I have been gritting my teeth and trying to wrangle webmail into working for me until I can find another alternative.

I have tried re-entering the settings several times and just tried it again and it didn't work.

Is there a way to change the IMAP settings so that I don't automatically delete emails from Mac mail when I delete them from webmail? If there is any chance it will create more problems, I'd rather not do it.

Wow, I just found a solution on the Apple website page called Mail Settings Lookup. That specified port 587 so I changed the "use default port" (which listed 587 and two others) to "use custom port" and put in 587. Now I can send emails again from Mac mail.

All did not stay well for long.

Is there some way I can limit the messages that are stored on the Cox server after I have downloaded them to Mac mail? I am always nearing my storage capacity and trying to delete messages from Cox makes me want to kill myself. Webmail ** so bad that I avoid dealing with it until I absolutely have to. Today I am getting "trouble fetching message headers" errors and when I try to sort by "From," which would allow me to delete large numbers of emails in a row, I can't get the messages to load. If I scroll too fast, they disappear. If I refresh, they go back into being sorted by date. What sort of monster programmed webmail? It's not just useless, it is infuriating.

I have an IMAP account. Is there a Mac browser other than Safari or Firefox in which webmail might be more stable? I have around 3,000 emails stored on the server and I could delete most of them if (a) that process didn't also delete them on my mac mail and (b) I could get webmail to load and sort for more than a few minutes. My patience runs out after half an hour of trying and only being able to delete a few dozen messages because the headers won't load or I keep getting back to the top of the list.

I need to keep the IMAP account because I do use multiple devices.

I notice that (so far) you have not addressed the shortcomings of webmail. The storage limit issue is going to continue to cause me problems because there is no other solution but to delete messages directly from webmail, correct? It doesn't sync the other direction - deleting emails from Mac mail doesn't delete them from the server.

They do seem to be syncing now. Earlier, I was having such difficulty getting messages to load in webmail that I couldn't tell what had been deleted. But the total numbers of messages seem to be the same now.

Does Cox offer larger storage capacity for emails?