For these who similarily suffer from having to use Googlemail at work. If anyone else has more of these, please do share.
Deactivate the spamfilter
The site admins can do that. Otherwise, you will have work-relevant eMails, for example from your own OTRS system, end up in Spam (where you don’t see it, as their IMAP sucks) and deleted without asking 30 days later. (AIUI, the only way to get eMails actually deleted from Google…)
Do not use their SMTP service
Use your own outgoing MTA. This brings back the, well, not feature but should-have-been-granted-but-Google-doesn’t-do-it-anyway that, when you write to a mailing list, you also get your own messages into your own INBOX.
Calendars…
I have no solutions for this. I stopped using the Googlemail calendars because they didn’t think it a problem that, when I accept an invitation in Kontact (KDEPIM as packaged in Debian sid), the organiser of the calendar item in the sender’s calendar (for which I do not have write permissions) changes to me (so the actual meeting organiser cannot change anything afterwards) and/or calendar items get doubled. I now run a local uw-imapd (forward-ported to sid by means of a binNMU) for sent-mail folders etc. and a local iCalendar directory for calendars.