Hi, You can do that all by adding template override actually. Please follow this video if you don't know how to do that
https://www.youtube.com/watch?v=tMB97xfYQfY and for your questions :
1) How can I get the article title to link to the assigned link in the "Images and Links" settings of the Article instead of the article details?
Did you mean you want to use Link A, Link B, Link C instead of single article link?

if so, you can add this code in your template override :
<?php $articleLinks = json_decode($item->urls); echo "<a href="/.$articleLinks->urla.">Link A</a>"; ?>
2) Is it possible to show html (small image w/ link) in the Intro Text? - It shows in the details page but not the intro text (and it is within the intro chars limit)
after you have created template override, find this part :
echo JHtmlString::truncate(strip_tags($item->introtext), $introtext_truncate);
change that to
echo $item->introtext;