it seems that you already managed the setup of the tobit "mail access server". For security reasons you should create a a tls certificate using tlscert.exe located in the directory \david\util\windows\tlscert. After successfully creating the certificate, rename it to "macert.pem" and copy the file to \david\apps\maserver\code. Set the option "TLS Usage" (TLS Nutzung) to "if possible" (wenn möglich" in the "mail access server" configuration. Afterwards you could connect to the "mail access server" via IMAP SSL on port 993, setting up right port forwarding ist mandatory.
I would recommend using the smtp server of the domain hosting provider instead of using the Tobit "Postman", also for security reasons, e.g. spam...
The problem about sent mails could be fixed within your mobile phone imap client, there should be an option for setting the location for sent mails, e.g. on an iphone you can choose between saving on iphone or saving on imap server.
The last problem about deleting messages via imap could be fixed by the option "delete messages via imap directly" (Nachrichten per imap direkt löschen".
Finally restart the "mail access server" service on your david server after setting all options!
good luck