John Havlik

If you using one of the list types for the markup (ul or ol) you will need to use CSS to make it display as a breadcrumb trail instead of a list.
Something like the following should get the breadcrumbs appearing next to each other (note it assumes the wrapping tag has the class of breadcrumbs):

.breadcrumbs li
{
	list-style: none;
	margin: 0;
}
.breadcrumbs > li
{
	float: left;
	padding-left: 10px;
}

The later portion of the following article is where I took this from, and has some more detail as to what the CSS is doing: https://mtekk.us/archives/guides/vista-like-breadcrumbs-for-wordpress/

So, adjusting the browser’s URL bar based on the attributes selected for the product is not something that is within the scope of breadcrumb trails or what Breadcrumb NavXT does. To update the browser’s URL bar you probably need some JavaScript that runs and adds components to the URL when each attribute is adjusted.

The first site you linked to doesn’t seem to have a breadcrumb trail showing up for me, so I’m not exactly sure what you’re trying to replicate. Assuming what you want to do is have product variations represented in the breadcrumb trail, that could get messy quickly. Breadcrumb NavXT generates location breadcrumb trails, which subscribes to the idea that resources have one true location. Thus, having the variation influence anything before the current item breadcrumb in the trail isn’t going to really fit the location breadcrumb model. Additionally, I’m not exactly sure adding the variations to the end of the trail makes a ton of sense either. Technically, either are possible to achieve, but you’re going to need custom code to pick off what variation is in effect and add that breadcrumb (though I’m not sure what it’d link to exactly, maybe an archive for all products of that variation type?).

Since root pages are not truly a part of WordPress core, translating them requires additional code which is not present in WPML nor Breadcrumb NavXT. You can do this by using the bcn_before_fill action to modify the root page settings just before the breadcrumb trail is generated. This said, there is a extension for Breadcrumb NavXT that adds WPML string translation support for root page translation (in addition to the rest of the Breadcrumb NavXT settings).

What are you expecting Cat or Tag to link to, or represent? I ask as WordPress doesn’t have a concept of a root page for all categories or tags. Thus, Breadcrumb NavXT doesn’t create breadcrumbs for them (thus no Cat or Tags breadcrumbs). Everything is post (of any post type) centric, posts are ‘things’ while taxonomies are just ways to classify things. So, post types will have archive pages, and root pages, but taxonomies will not as taxonomies are just a way to organize posts (of any post type). So, Breadcrumb NavXT treats posts (of any type) as the more important thing and associates taxonomies with the post type (a term archive will throw in the post type archive breadcrumb of the primary post type associated with the taxonomy).

The expected behavior is Home > Term (category name, tag name) on a term archive page for non-static front page sites using the built-in Category and Tag taxonomies associated with the built-in Post post type. For a single post, the expected breadcrumb trail would be Home > Term > Post Name for a similarly configured site (note that the term breadcrumb may be several breadcrumbs if using a hierarchical taxonomy and the post is a member of a term with a parent term; that is the term breadcrumb will expand to represent a hierarchical term’s parent hierarchy, if present).

As a side note, it appears someone else is trying to do a similar thing (see https://wordpress.org/support/topic/custom-taxonomy-missing-item/), I don’t really recommend trying to do this as you’re going to be fighting WordPress in how it tries to do things.

Not directly, but calling bcn_display(true, false) and passing the result into something that strips HTML tags such as strip_tags() will probably produce a trail that doesn’t contain HTML tags so it should work within the title tag. So, in theory something like the following may work:
echo strip_tags(bcn_display(true, false));
Note I have not tried this so it may need additional code/adjustment.

Regarding not showing a tag or category, you can uncheck the “Hierarchy Display” option for the post type in question.

Looking at your site, it appears you have something configured in an odd manner. “Tags” is representing a the root page of your posts (you have the Tags page set as the Posts page within the WordPress settings under the reading screen). However, it appears you don’t have a static front page, and the Tags page just shows a tag cloud, which really isn’t properly fulfilling the role of the root page for posts/page for posts. So you probably don’t want to have a posts page set (and need to not have it set as your posts page to prevent Breadcrumb NavXT from adding it to the breadcrumb trail).