Hi, this is Ms Help from italki. It is such a pity that I just found out about this group.
1. Yes, if someone deleted their inbox messges, the messages will be deleted in both sender and receivers' inbox.
2. The chat is really slow sometimes. And the current version is provided by a third party. Our team can not change it as what we want. So in the future, we might redevelop a chat system ourselves. Actually, we have tried to launched a "new" chat system which is not stable at all. So we have to switch back the current version.
Thank you for your attention. We will try our best to solve this problem. And please post more suggestions or problems you have experienced at italki. We will check the group regularly.