Manual penalties can be checked for using Google Search Console.
There's also a free tool called Panguin by a company called Barracuda - Google it and you will find it. Take it with a pinch of salt, but it may identify key times where your organic traffic has dropped off. It could correlate with a search update.
There's a few things you can do to check for plagiarism - use CopyScape, but the free version is limited. You can also just search in Google for chunks of your text within "inverted commas" to see if anyone else is using your content or similar.