Is there such software ... the mobile phone is connected to the computer ... and then the mobile phone can control,,, screen shots, text messages, phone calls and so on on the computer? ...

It depends on the model of your phone. Generally, licensed mobile phones have a CD for you, which contains a PC suite. After installation, you can edit the address book, short messages (including sending and receiving) and multimedia in your mobile phone on your computer.

If you don't have a CD, you can also search the official website of your mobile phone online, such as:

From the official website of Nokia in www.nokia.com.cn: You can download the PC suite and software of your mobile phone model from the official website.

I'm not sure about domestic mobile phones;

If you have an Android phone, you can use 9 1 mobile assistant or mobile phone pea pods!