Is it okay to use the term "proposed method" in academic paper if I already done implementing the method? Or what phrase I can replace to this?
No. If the experiment is already completed, you would list what you did under the Materials and Methods part of your paper. You may editorialize at the end of the section, but it is best to propose detailed changes in the Discussion section. If your completed experiment did not offer the conclusion you were hoping for, that's where (Conclusion) you could add what you would do next time to make it better, in brief.
Yes, it's okay because it's a method that you are proposing to the readers. So you can write
The method proposed in this paper allows [...]
We have therefore shown that the proposed method yields [...]