All in one SEO (Search Engine Optimization) which is an SEO plugin.

No you do not have to upgrade as the standard version suffices, you also do not need to install MonsterInsights.

However nowadays WA recommends the SEO frameork. Setting Your Website Up for Search Engines (Using The SEO Framework)

It's actually AIOSEO and it stands for All In One Search Engine Optimization. It's a useful plugin that gives you some numbers related to your blog post. The upgrade to PRO is not necessary.

AIOSEO is a plugin to help you with Search Engine optimization which is what SEO means.
As for the plugin no you do not need to make any payment that is their way of trying you to pay when the basics are enough for you which is what WA teaches.
No need to buy the pro version nor any other options they give you like monsterinsights etc.

Hey Abie got you covered.
Lula

To add a website:

Click the Me icon top of your LinkedIn homepage
Click View profile
Click Contact info in your introduction section
In the pop-up window that appears, click the Edit icon
In the pop-up window that appears, click Add website
Copy and paste your website address into the website URL field.

Just click the PEN icon beside the dollar sign on top of the page.