vBulletin has a calendar by default.
vB.org's calendar has mainly birthdays in it, but that would be up to you to fill it with events.
There are different Chat solutions available for vBulletin, or that can be integrated with vBulletin, ranging from Flash solutions to IRC frontends. Search the forums here and you should find a few.
A contact page isn't really needed, as your members could fill everything into their profile and it would be available at their members page. Yours looks like this:
https://vborg.vbsupport.ru/member.php?u=105302