ok first thing to do to check if you have been sanboxed is to use the site: string in google search.
example site:yourwebsite.com
If your website shows up first your not sandboxed, If it shows up but it's lower down the search results, you've got a Google penalty.
If that is the case you will need to disavow your bad links or check your anchor text ratio in ahrefs, majestic or any other tool you might use.
I can't give you a proper analysis without knowing your site.
As for Market Research well that's a lot easier for me to talk about.
You'll need the following tools, Similarweb firefox extention and a follow.net account.
Install both of these and visit all of your competitors websites. The free options of both of these will give you
some useful information you can use to see where the traffic is coming from and what keywords they are using.
Some of the info you will get include: Traffic = Organic or Paid, Keywords, banners, Ad copy, Social signals, Social mentions etc.
If you follow sites on follow.net they will send you emails anytime your competetion makes posts or are mentioned.
Another thing worth doing is getting your competitors backlink profile and seeing how many of those links you can get yourself.
There are free tools for this, it would just be a lot easier to buy a gig on fiverr to have your competetive analysis done from someone who is paid member at semrush, ahrefs or majestic if you don't have the funs for their membership.
If you can copy all of your competitors moves and tweak them to make them better you start to put yourself in a really good position.