Hi there,
Unfortunately, the login credentials are not correct and we could not access your website and I am not sure the website URL as you did not send us the correct URL.
We will not be able to help you to identify the problem as it is something that is caused by your customization. You need to double check that yourself. The thing that we can show is our browser console log which is full of the errors like this:

You need to make sure that the customization that you have done is correct.
The reason that the search icon goes to the next line is that there is not enough space for the menu items that you have when there is the sidebar.
You need to make sure that the padding between items is smaller. A CSS code like this may help:
.x-navbar .desktop .x-nav>li>a>span {
padding: .875em 1.25em;
}
Change 1.25 em to whatever size that will be better for the sidebar case.
Finally, I see that you use the Autoptimize plugin which minifies the assets of the theme and the builders which will cause problems as the assets (JS and CSS files) of the theme are already minified and using the plugin will have the double minification effect which will ruin things.
You either need to avoid using the plugin or check the assets of the theme and exclude them from minification process of the plugin.
Kindly open up new threads for additional questions as it will help us to focus on each issue and give you a better support which you deserve. Having a long threads makes the maintaining job harder and also it will be harder for the other customers to find the correct information if they have similar issues. You are always welcomed to reply to this thread to follow up the same question.
Thank you.