Does anyone know the css I need to add to make the search icon sit besides the NEWS menu item?

http://barefruit.com.au/dev/
Sorry that is the page.

I am also trying to figure out the code to make the header sticky.....the rest of the pages the header is stuck to the top, but the homepage it still scrolls.  What css do I have to add to make it stay put?

And I missed the sticky header.

I can't see any sticky menu in any page.

for the search to stay along the  top and also to stop  theme updates overwriting your changes install a plugin in called "simple custom CSS" from here:
https://en-gb.wordpress.org/plugins/simple-custom-css/

this will allow you to overwrite the styles without messing with the code and when updates for the theme come along it will still hold.

Once installed there is a new option under appearances "simple custom css" , go into that and add the following:

.topmenu_switch #topbar_right
{
    float: right;
    margin-left: 32%;
}

and save it.  the search box will now stay along the top (and work on mobiles)

for the sticky menu I would use a plugin such as:

https://wordpress.org/plugins/sticky-header/

otherwise you will need to go into the code and add stuff , and then you will have to create a child theme to stop it being overwritten when an update comes along.

I have created a child theme so I am happy to add code to the css
So what do I need to do to the homepage to make the header STICK

Thanks Pankja yours worked, but NOT RESPONSIVE so I changed it to
.topmenu_switch #topbar_right {
    right: 10%;
    position: absolute;
}
.topmenu_switch #topbar_menu {
    float: right;
    margin-right: 5%;
}

Thank you

chiltern, yours didn't include the search icon moving responsively either, or didn't work at all, but the first choice worked, but needed responsive coding

Nice help thanks

Glad to help 👍