BuddyPress.org

I’m not aware of any that integrate into BuddyPress.

Well, there are several Group chat rooms integrated well with BuddyPress.

When you choose, you need to consider the following:
1 – You can install one on your server, but if you have more than 10 chatters, that will probably load your server. Most shared hosting services, do not allow to install a chat on the server as it is high cpu/mem consumer. In addition, sharing files is dead slow.

2 – I recommend a group chat hosted service, it will offload all activity to a remote server, bandwidth is not a consideration. They work with CDN, so everything is pretty fast.

As for your question:
I am very much in favor of RumbleTalk chat plugin, works very well and integrate with your users base.

– Ability to send any files (anything from videos, photos, music, etc.)
Yes -You can upload files, pdf,excel..etc, I think any file, but they have size limit
– Ability to text chat
Yes
– Ability to video or voice call to a friend
Yes – they have private chat (you need to allow it in the settings), you must be in ssl to use it (WebRTC)
– (Optional) ability to add other friends or users to the chat
Yes – you can allow facebook/twitter friends
– (Optional) ability to screen share (desktop sharing)
No – no screen sharing

Hello Michael Lanfield,

Please contact with us at sales@cometchat.com with your requirements and we’ll help you out.

Regards,
Robert

This is a great chat plugin and very facebook-ish, although no video, but chat has multichat function etc.

http://codecanyon.net/item/wordpress-buddypress-users-chat-plugin/10776067

Apphitect IM has SDK Chat support for android, iOS & web.

Don’t pay month by month, alternatively just own the collaboration tool for your business. It is one time payment & access the full control.

Apphitect IM has come with advanced in built features are

Provides own SDK
Customizable SDK to serve specific business needs. Chat API & SDK’s

Own Cloud & server
Host data on a cloud server to scale up your instant messaging mobile app’s accessibility & scalability.

Direct and Group video chat
Create chat groups with any number of members to communicate real time.

Lightweight Application
IM solution that performs great with less strain on your smartphone’s processor

voice and video conferencing
Communicate with a personal touch with voice/video calls on the chat app

file/call/ group screen sharing
Share real-time location, screen, data details through the chat app easily.

Hello.

There is a solution that you exactly looking for.
It is a chat plugin for BuddyPress and WordPress.

This chat has three basic feature such as:

• Text group chat between users
• Text private (one-to-one) chat between users
• Online chat support (chat with customers)

Besides these functions, the ImbaChat has also:

• Sharing files (any type of file)
• Chat moderation
• Video chat (group and private)
• Audio calls

The ImbaChat basic functions are free. Pricing for the additional features is from $4.99 to $19 per month. Easy and quick installation on BuddyPress. Full integration with the user base of your website.
Visit the official website of the plugin to learn more.