starlight Hi
1 &2 ) Have made some changes in the css accordingly :
/* adding another search position */
.t3-topbar .top-mid{position: absolute;right: 14em;text-align: ;top: 0;}
.module-search .inputbox{display: block;float: left;height: 47px;line-height: 28px;border: 0;border-left: 1px solid #e5e5e5;box-sizing: border-box;width: 200px;font-size: 16px;padding: 10px 24px 10px 48px;}
@media only screen
and (max-width: 600px){.t3-topbar .top-mid {position: fixed;top: 0;left: 40%;}.module-search .inputbox{width:100px !important;}.t3-topbar .top-mid{float:left !important;margin-left: 2em;}.t3-topbar .top-mid .module-search .inputbox{background: #f8f8f8;}
}
3) To be precise and avoid ambiquity, Can you provide screenshot marked with annotations showing the relative issue so as to review the same
4) Have tried scrolling in responsive mode, The issue doesnt appear for me. Kindly check again
5) Not sure as to how to add the same functionality to 3rd party search module as it is inherited through JS
6) To be precise and avoid ambiquity, Can you provide screenshot marked with annotations as I am unable to see any such text