For your site ranking:
There is a free and interesting site called Alexa.com, which is now a subsidiary of Amazon.com. It measures your site’s ranking (popularity) in the world, or in a specific country. You simply go to alexa.com, type in the domain name, and it will give you the traffic statistics for that website.
PSPinc has a popular free Japanese learning site which was ranked 251,277th place as November, and 32% of its traffic comes from United States. It also shows things like bounce rates, related sites, average daily page views, and duration on the site per user.
For your mobile performance:
Analyzing your site’s performance shouldn’t be based solely on traffic; you should also assess its quality. And a big indication of a good quality website is how user-friendly it is on mobile devices. Google has repeatedly stated it gives more favorable search engine results to sites that are mobile friendly.
You can go to Google's Mobile-Friendly Test Page and type in your website address. It will tell you if your site is mobile friendly and also show you how it appears to mobile users.
For your domain history:
Archive.org is a non-profit digital library of all previously published websites. You can enter a URL into the search field and find out a lot about its history and when it came into existence. Archive has captured the history of over 270 billion web pages across a 20-year span. The site was founded in 1996 and our website pspinc.com was first captured and stored in their database in December 1996!