Hi propolis
1st) That's template logo image, to disable it add to your custom.css file
.logo a {
display:none!important;
}
2nd) Grey line is showed only on active menu , if you are in home page then it is showed below home menu item.
3rd) add to your custom.css
.navbar-default .navbar-nav > .active > a:before, .navbar-default .navbar-nav > .active > span:before {
background:transparent!important;
}
4th) that's the footer add to your custom.css
.t3-footer {
display:none!important;
}
If you do not have already a custom.css file then create a new one in /templates/ja_insight/css/ folder
Hope it helps