Hey Grace,
Regretfully, we don’t have an option to change the case of the sub-menu in the Original Header. I’d recommend that you create a custom header using the Header Builder and add Navigation Inline element inside it. The Navigation elements have an option to change the case of the text. This is the official solution.
If you wish to continue using the Original Header, you’d need to write your own CSS code. I’ll provide a starting point for you but just note that we will not provide more custom codes after this and we also will not support issues that will arise from the use of custom codes.
With that said, please add the following code in Theme Options > CSS. You can learn how CSS works here.
.x-navbar .x-nav li>a {
text-transform: uppercase;
}
I’ve tested that code and it’s working. If that doesn’t work in your site, it means that there’s broken CSS somewhere in your site or there’s a conflicting code. If that’s the case, you really need to build a Pro Header. Otherwise, you need to consult with a developer.
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Regarding the house icon, are you referring to the Breadcrumbs? If so, that indicates the home page and it’s a common display for websites. There’s no option to change that so the solution would be to create a Pro Header and add the Breadcrumbs element. Using the said element, you can display text instead of just the home icon.

If that is not what you mean, please provide the URL of the page where we can find the home icon you’re referring to.
Hope that helps.