I took some time to look over your template issues and also looked over the boemia demo template. In trying to make sense of it I'm wondering if there might not be some issue with your site's css related to the mobile responsive stuff like bootstrap, etc. The demo site scales pretty well, paragraphs are all seen with no side to side scrolling needed. The current site seems like the paragraphs and div's are 'stuck' at a wider view when the screen is sized down. Also, the mobile menu doesn't appear and the search box should be popping to the top on smaller screen sizes like in the demo.
I wonder if some of the css didn't quite get applied assuming it's a child theme that's activated? Or perhaps theres some custom mods to the css that are interfering/disabling the bootstrap css that the demo site has.
There's some different ways to approach the issue. One would be to contact the template provider and ask them for assistance directly. It could be they will know real quickly where the issue lays. Perhaps by providing them with a login to see.
Second way, I'd recommend removing any css modifications made to the template after installation temporarily to see if it fixes the mobile menu and the div's scaling down properly. If it does, then re apply customized css one by one until you see the problems reappear. It just seems like something's missing or something is interfering with the way the template responds. I was about to chalk it up to the template provider as the problem, but the demo site seems to work well.
On the lesser issue of the icons not appearing in a neat row in IE, it seems that since the block of icons was done using spaces instead of css padding, there's one two many spaces in between the icons for IE's taste. Even though the template width should be standard in all browsers, for some reason, IE feels there's too much and drops the last icon to the next row. When i remove some extra spaces via the firebug inspector the icons all line up in ie.-which is an easy fix :)
However, the mobile menu missing, the search box being to the right of the logo, and the paragraphs running off the page rather than staying within the browser window are indicative of some custom css interference or some css missing, etc. Sorry for the long message, but this is my best guess. Any one else is welcome to chime in :)
Please keep me posted :)