1) This will fix it for mobile - tablets use the same view as desktop, so it should be fine there!
2) Yup! Edit header.php with a child theme and locate (the second spot for header menu, so it's not topbar):
<div class="nav-text"><!-- put your mobile menu text here --></div>
And do like:
<div class="nav-text">Navigation</div>
or something similar. And then add some css styling as you wish:
#nav-header .nav-text { color: #444; font-weight: 600; }