yes you can ! 
ok, itâs quite simple when you know about it :
open your template, and make a dimension. you can make it in the grey if you want. Here, you adjust all the parameters of your template. lines, length, colour, all.

then use the eyedropper on this dimension. and from now on, all the new dimensions I place will have this parameter (anything from the line style or the dimension style panels). If you save your template with this âready madeâ dimension on the side, then all you need is to eyedrop it and bam, ready to work.
let me show you
here, first is vanilla,
second I adjusted the top lines length and width, and I moved the textbox on the side. then eyedropper
thirds, you see, some of the parameters remained.
Unfortunately, and it answers some of your other questions, the position of the text is not a parameter in one of the side panel (I mean the distance between the text and the line). and it wonât be kept while using the eyedropper tool.
And yes. I forgot to do it, but if you change the text (size, font location under / over the line) it will register with the eyedropper.
so here on the 3rd line I put some blue lines, a purple text in 6pt and voilĂ . If I use the eyedropper on it, then all my future dimensions will use this template.
as for moving the text box closer to the line, I donât see a way to do it by default.

I can manually move it (then make the curved line white), but as I said earlier, the eyedropper trick wonât reproduce it because itâs not a parameter, itâs me (or you) physically moving the text box. 
as for the snapping dimensions.
snapping side by side s quite simple, layout keeps the inferences point, so you just need to pull the dimension next to the neighbour, and itâll snap.
what you can do if you want several dimension to behave as a group is select them and group them, like you would in SU. now if I pull to make the group longer, the proportion will be kept.