The company sent me the contract, I signed it and returned back to them, so now they should sign and send me the copy.
In Germany, what if they decide to not sign and withdraw the process. What one can do in this situation, is there any law?
This may or may not help you, I am aware that common law and Germanic law have very different origins, history and consequence; but, since I know nothing about German law I will give you the common law answer.
An essential part of a common law contract is the offer and acceptance. One party makes an offer and the other party accepts it. Acceptance can be done by word (verbal or in writing) or action - if the parties act as though there was a contract then there is a contract.
By sending you their terms they have made an offer to you; by signing and returning it you have accepted their offer: you are now parties to a binding contract. There is no requirement for them to sign it or send it back.
However, if you amended their terms then you have not accepted them , you have made a counter-offer. They can accept them by word (sending you a signed contract back) or deed (doing what the contract says they should).
Offers can be withdrawn until they are accepted; after that there is a legally binding contract.