This is the navigation tag. From what I see, you don't yet have a field for the image gallery link. I believe this is the tag you want to use to add it.
I don't think the arrows themselves would impact the CSS. If what you mean is the fact that the labels that include the arrows are side-by-side, then yes. That is what I was referring to has the horizontal group.
What the sections link to shouldn't impact the CSS. For turning the header indo a link, try just using the normal link syntax. If that doesn't work, then you will probably have to switch to using a navigation tag instead and leave the horizontal group without a header tag. As for the image gallery, the navigation tag should be able to handle regular MediaWiki markup, including use of template parameters.
The tabs thing seems to be resolve to me. I assume you figure it out yourself?