The code you are showing has nothing to do with your question. And your question has more to do with HTML.
When you are using an input element (html) then the form action defines where to go. You don't have to return to the home page.
<form name="input" action="homepage.php" method="get"></form>
You can skip (or leave blank) the action attribute to redirect to the current page. With PHP you can determine what html input control submitted the form and you can use that to do something, like redirecting to other pages.
You can also use links with an image:
<a href="http://www.yoursite.com/currpage.php?lang=en">
<img src="lang_en.png" />
</a>
Get the 'lang' parameter to update the language.