Hi Guy,
China is not the China of ten years ago. If you come here, you had best recognize that it is new, modern and follows set laws. Any ideas toward bending or breaking existing laws should be the furthest from your mind right now. China will not accept this kind of behavior.
Let's see what I can do for you...
1. Is there any program/school in Dalian that offer only weekend class that he can sign up?
There probably are. Dalian is a reasonably sized city. However, would weekend classes be enough to qualify for an educational visas, I do not know. I would guess not. You would need to enroll in a school program that would fill out the paperwork for a student visa or support you filling it out. You will need to do some research on local schools to find out.
2. Can he apply for the a program there, pay for the school but not attending?
Maybe, but I would doubt it. China is a nation of business-savvy nerds. They would "smell" this out in a heartbeat. i would not advise any creative escapades along these lines. You could risk all kinds of complications.
3. Is there any teaching English job that only requires a few hours a week? It can be free. He doesn't need to be paid. He only needs visa sponsor.
Also unlikely. To teach English you will NEED to obtain a Z-visa. That requires a university degree, a ESl certificate, two years of work experience, and a school that is willing to sponsor you. Any school willing to do this will expect work or labor for their effort.
4. Any other suggestions would be greatly appreciated.
There are other legal options. You should look into them.
[1] Get a ten year visitor visa. Come but don't work. The requirement would be that you would have a multi-entry requirement. Today, most visitor visas are of short duration, however longer duration visas are available, but are granted on a conditional basis upon interview. Go ahead and try to get one. There is nothing preventing you doing this but fear.
[2] Set up a business within China. You can do this by setting up a WOFE. You don't even need to make any money, but you will have to pay your yearly taxes. You would need to set up an office in China, and do all the paperwork. With this in place, you can come into china on a working visa (not a Z-visa).
[3] All Z-visas' require sponsorship. If you are going to be legal in china under a Z-visa you will need to work. Some schools will provide you with a Z-visa with only a 20 hour to 30 hour work week. However, you will be locked into a two year contract. i would not advise you breaking it. If you want to come to china YOU WILL NEED TO work. China is a nation of hard working nerds, they just cannot understand non-working folk. Everyone's parents works. Everyone works or studies. It's the Chinese way.
[4] Go to school. Find a school that offer night classes. One parent can be with the child during the day and then go to school at night. The visa will allow for this.
Best of luck.