to check traffic, you first need to track your visitors, which could be possible with the helps of analytics like Google Analytics, clicky, piwik etc.. As you are saying that you want to check traffic without using anything I assume that you want to check your competitors traffic or a traffic of website that you do not have access to. In that case, you have to check alexa, similarweb, semrush and other third party software tools. These may not give your exact traffic and other things, but you will get some idea.
Coming to checking backlinks, there are too many tools like ahrefs, majestic, ose, moz, seoquake etc.. which you can use to check backlinks. Small seo tools will also show some backlinks, but may be not accurate completely.
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