There are commercial solutions such as OSASync, but these do not support simultaneous sharing of one PST file. Outlook (and the file format) does not support it.
No, but you can sign up one generic user to Exchange Online. Then you can set up multiple computers to share this e-mail account as a delegate. The use case would be a help desk or sales team that are answering e-mails sent to a centralized e-mail.
