Can I use my mobile phone to video or send text messages all over the world?

Mobile phone (telephone, not third-party software) video itself needs the support of communication network. Currently, only 3G networks are supported. Considering that 3G is available all over the world, it is definitely not universal.

As for SMS, as long as there is a network, it should be supported unless the country is not open.

As for QQ, it is a software that needs network support. As long as you can surf the Internet and there is no local ban on QQ, you can definitely use it.