How to save my academic career after ending up in a deeply problematic lab for PhD?
Deciding to leave one university for another is in my belief, beyond the scope of asking strangers on the internet. However one thing stood out.


  The lab I am working at has several issues and there are many deeply unethical things going on.


If things are as egregious as you claim, you are beyond, "should I leave" territory and cross into "what are my country's whistle-blower laws"? Is your lab injecting subjects with unknown substances or diseases without their knowledge? Is it stealing or utilizing funds in an unscrupulous manner such as buying personal items?

If things aren't as serious as claimed, I don't see why you couldn't have a sit-down meeting with your researchers and inform them of your dissatisfaction and hope things turn around. If it comes to applying to another program, you can always inform your potential institution of the shortcoming of your current situation.