MacBook Pro Safari Version 10.1.2 (10603.3.8)

I have Safari Version 10.1.2 (10603.3.8) installed on my MacBook Pro (Retina, 15-inch, Mid 2014). Is the latest version of Safari updated automatically on regular basis? If not how do I update my version of Safari. I have 2 problems:

1. Regularly, when I visit certain websites I am asked to update my browser. For example, (a) I get the following when logging in: "Browser Alert -  It looks like the version of Safari you're using may not offer you the best Online Banking experience. We suggest you update your browser to the latest version before continuing"; or (b) "Your web browser is out of date". When I look in App Store, no Safari updates are available.
2. Certain websites have stopped opening, that used to open in the past. For example, the following message appears: Safari can’t open the page “https://en.wikipedia.org/wiki/Goods” because Safari can’t establish a secure connection to the server “en.wikipedia.org”.

To get around the above problems I have to switch Google Chrome.

I will appreciate any help.

Regards