1. Not sure, but I think there is an event modification. You may wish to check this first.
2. Link and Download Manager and I think Downloads II or something are available:
https://vborg.vbsupport.ru/showthread.php?t=166094
That mod will probably do most of what you asked for.
3. There's a calendar feature built into vBulletin, but the quality of it is debatable. I am not sure if an event mod integrates with it.
4. You can use any gallery script for this. Either bridge Coppermine or Gallery with vBulletin, or use Photoplog or Photo Post. They come with the usual full permissions system.
5. Need more information on what modules. Others can probably help more with this.
6. Everything can be edited through the Admin CP, including permissions and modification set up as well as styles.
As for blogs, you could use vBulletin Blog, or you could just use a sticky or announcement topic. Live chat can be added, as certain mods are for the integration of scripts like Flash Chat with vBulletin. The permissions you want can all be done with usergroups and the paid subscription feature. Hope that helped.