We have Exchange as internal mail server, also we have gate where we plant to install Dovecot, also we have external mail at servers such as yahoo.com ort yandex.com. There are some mailboxes at Exchange, for example: user1@internal.ltd to user10@internal.ltd. There are some mailboxes at Ynadex.com, for example: personel1@external.com to personel10@external.com.

1. For messages flow: We need that Dovecot would act as at least transparent IMAP proxy for Exchange/Yandex and vise versa. For incoming messages - some messages comes to personel5@external.com located at Yandex.com, then Dovecot gets it from Yandex using IMAP IDLE, tnen stores it locally (where Dovecot is installed) to MySQL (using DBMail) or at least maildir format and after that sends it forward (using IMAP PUSH) to appropriate account user5@internal.ltd or triggers (signals) Fetchmail to sends forward it to specified Exchange acoount. And so on - for each external/interla pairs of accounts (Yandex.com/Exchange) . For outgoing messages - Exchange send out it using Exim4, Exim4 stores it locally (where Dovecot is installed) to MySQL (using DBMail) and then Exim4 sends it out to Yandex.com and in the same time Dovecot uploads this message to Yandex.com to "Sent" folder. And this messages is sent through Yandex.com.
2. For messages storage: When messages are deleted at Exchange, it are deleted from Dovecot (MySQL storage) and deleted from Yandex.com as well. Or when messages are deleted from Yandex.com, it are deleted from Dovecot (MySQL storage) and deleted from Exchange as well.

Is it possible to set up Dovecot and may be some other soft (Fetchmail, imapsyncd and so on) to get point 1 working or point 1 and point 2 working ?