There are third-party addons which you can purchase such as CometChat, ArrowChat, etc. Those are live chatting addons, btw. (that's all that I can think of atm)
I've seen a gallery add-on (not sure if it still works so you have to do a search) and I've heard one is being developed by a third-party developer (King K or something is the username).
Search :
- http://xenforo.com/community/resources/
- http://xenforo.com/community/forums/add-on-releases.72/
Keyword "gallery" search Via Resource Manager (should find some results) : http://xenforo.com/community/search/2027177/?q=gallery&t=resource_update&o=date
Also, for videos you can use this addon: http://xenforo.com/community/resources/8wayrun-com-xenmedio-media.97/
Although I've only used it to grab YouTube videos but I'm not sure if you can do more with it, 
...?
For a gallery add-on or something?
Yes!
Thought you meant threads alone.. Nope (from the core features), I don't think you can (if you want one post from a thread to be on a separate page to be shared Via Twitter/FB).
http://xenforo.com/help/cache/
There is the build-in xenForo Trophies but I'm not sure if that's what you want.
FaceBook - built in core.
Twitter - I've seen an add-on and several forums using it.
http://xenforo.com/community/threads/wordpress-3-bridge.5398/
I have not tested to see if it works but the developer is active,
I've read that a mobile theme is planned for the future. You can install TapaTalk and ForumRunner as well, 
TapaTalk - http://xenforo.com/community/resources/tapatalk-forum-app-for-xenforo-ios-android-blackberry-mobile-app.263/
ForumRunner - http://xenforo.com/community/threads/announcing-forum-runner-xenforo-iphone-ipad-android-app.12070/
Yes. Have a look in the Resource Manager : http://xenforo.com/community/resources/categories/styles.29/
You can always search Google for "xenforo themes", "xenforo skins", etc. (just make sure that you don't run into a warez website)
