Hi there,
I saw you were using the Zerif Lite theme on your site, so I installed it to do some testing. I saw the same thing regarding the profile picture when using Zerif Lite:
Link to image: https://d.pr/i/2L38RR
But then after switching back to Storefront, the same reviews were displaying differently:
Link to image: https://d.pr/i/lbjAYb
So, it seems the display of the reviews is being affected by the Zerif Lite theme. I would recommend reaching out to team behind that theme to ask about this.
That said though, regarding the links — entering a <a href="x">test</a>
link in a review, or just copying/pasting the link itself, still rendered the clickable link in the review afterward even when using that theme.
Something on your site must be changing that behavior. I would recommend a full conflict test to try to narrow down what is causing that: https://docs.woocommerce.com/document/how-to-test-for-conflicts/
I hope that helps!