There is no impact

for you to land next job since it is unlawful for your previous employer to disclose anything besides 职位，工资，和离职日期.

There is no way for your future employers to find our you were fired via official channels, such as HR department unless you tell them.

1. You don't need a lawyer. You should apply for the unemployment benefit immediately since you are eligible as you have found out already.
2. You need to pick reference carefully from your previous employer to ensure s/he does give the positive feedback.
3. You have short employment history, however I still think it is fairly reasonable to tell people the position was eliminated due to project was cancelled or company was doing reorganization, and unfortunately you were affected. As you can see, you are not lying by saying the statement above. As the performance review is subjective and opinionated, you should be confident to demonstrate all the good work you have done during the interview process. If you do well for all the technical questions, you will be able to get hired easily.