I found some high DA/PA sites which offering free backlink to increase link popularity, is it bad? or againts rules for links building?
"Free backlinks" are usually low quality, so avoid them. Which sites are you specifically talking about?
You only want links on sites that are quality sites people will actually use and sites that are relevant to your industry. Sites that are advertising or offering to give free backlinks are most likely not the sites you want to be on.
No matter what, when getting backlinks, you want the referring site to be: Relevant to your niche From clean sources with natural link profiles Decent PR/PA/DA Whether their paid or free, that should be the criteria you're looking for. Also, try not to look at "increasing site rank and DA/PA" as any kind of goal. These are 3rd party metrics that are loosely tied in to the goals that you really care about: SERP rank and traffic.