Eligibility to work in Germany

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(Moderators please note: Though the word "job" is mentioned in the following post, it still isn't a job related post. It essentially is an "immigration to Germany for work" type of post. So, for heaven sake, don't move this thread to Jobs forum)

Dear forum members,

I am eyeing on contract jobs in Germany. The usual big limitation is that I am not from the EU. What possibility do you suggest for me. Could you forum members advise me upon my following vague ideas:
1) There is no work visa for Germany that can be obtained without having a job offer, is that correct?
2) I suppose that in Germany, like in most countries, people do contract jobs by setting up their own limited companies. Is that right?
3) I know that in Czech Republic, one way for non-EU foreigners to be able to live in Czech R as well as to be able to do contract jobs is to set up a limited company, get a business license, and based on the business license get a visa that authorizes one to do business (or contract job) in Czech R. Question: Is the same concept valid in Germany?
4) If the answer to 3 is no, then, my question is, as mentioned in 3, if I set up a limited company in Czech Rep, get a business license for Czech Rep, and based on it I get a visa to do business (or contract job) in Czech Rep, THEN, based on this, would I be permitted to do business (or contract job) in Germany?
Thanks for your wise advice.