Hi John,
Try this to change the width of the search field:
input.search-field {
max-width: 150px;
}
Not sure how to replace the text by an image – this topic is probably more suitable for the plugin author.
On another note, are you only wanting search in secondary navigation? If so it might be better to use primary navigation as the secondary navigation. Tom made suggestion here: https://generatepress.com/forums/topic/move-navigation-search/#post-275175