Not reflecting my parameters and even not showing at all

I think it can cause padding or margins for img tag, or max-width=100% case in template. For example, it overrides all img tags, not for special.

In object inspector find img tag in map (for example zoom control), check its properties. If it's overridden (for example you can see max-width:100% or padding to -1000, it can cause that you can't see images (map tiles).
If yes - just add in template CSS file to end overriding for img/svg tags for elements in map div, or for elements for divs with map classes.

As for RocketTheme - check my forum. Sometimes it breaks my code: map is exists and you can see it, but map objects - not. It can caused by its plugin - it can add extra line break and closing div or script tag in infowin content HTML body.

Empty space instead of map can be caused not initialized map.
For example, by default I use onload function to initialize map. If the other extension use it, it can override my call.
In this case try to change map initialization type in component options to JQuery ready event.

Yes, I guess something is not initialized or called properly.
Not sure it's only a question of CSS. See those 2 captures of the code (OK.png and not-ok.png).

In one case I get an image and sizes, in another case I get a call for the right service.

Sorry, I forgot to mention I tried onload, domready and jQuery ready event techniques, which didn't change anything.

I can't analyze code without page, because I can't understand context problem.
Ie.
For default template - OK. When you change template for map menu item. Is it OK,
Or you trying use module and have troubles.
In every question I need context - component call (menu item), or module.

As for code - I can see 100% height, and a lot of nested divs - it can collapse map div and you can't see map, without any space. Because for 100% height you have to set 100% height for every div above yours up to displayed block div. In other case it collapse.
For example, you can apply my Full screen template for map menu item with width = 0 (100%) and height = 0 (100%) and you'll see full screen map.

Is there a way to send you an URL in a confidential way ?