But I'm kinda stuck: total CSS-n00b here.
What I'd like to do is add some better formatting, kinda like the forum's code-tags for instance, a bit less vertical white space, and some headers. But again: total CSS-n00b here

Well, let me try.
Go to your
http://addresses.loyce.club/css/all.css file
You will find this:
.xBlank {
padding-top: calc(4rem + 74px);
padding-bottom: 11rem;
}
Delete it, and add this:
.xBlank {
padding-top: calc(2rem + 74px);
padding-bottom: 2rem;}
This will fix the vertical white space.
About code tags, you just need to add <code> </code> where you want to
look like code. 35hK24tcLEWcgNA4JxpvbkNkoAcDGqQPsP, like this, right?
Just add
<code>35hK24tcLEWcgNA4JxpvbkNkoAcDGqQPsP </code>
<code class="balance"> 25550215765875</code><br>
<code>
3KZ526NxCVXbKwwP66RgM3pte6zW4gY1tD</code>
<code class="balance"> 10185724750535</code>
and add in your Css for different colors:
code.balance {
color: #17324d!important;
}
You will see this effect. I think it is what you said.
If you want to get completely rid of vetrtical space, delete the "xBlank" class from this DIV, in the HTML:
<!-- Just remove or copy the whole div/p/a/ tags from the (--start-- to --end--) -->
<div class="xBlank bg-default">