Should be a simple fix. add a value attribute to your form inputs with the field name as a tag, ie:
<input type="text" name="app-gallery-name" value="{app-gallery-name}" class="required text"/>
<textarea name="app-gallery-name">{app-gallery-name}</textarea>
And one more note. At one point you use a custom_fields loop to check for that one particular field. That’s a bit inefficient and yuo should be able to replace that with this:
{options:app-requested-booth-size}<input type="radio" id="app-requested-booth-size" name="app-requested-booth-size" value="{option_value}" {checked} class="required radio-but"/><label class="radio-but">{option_value}</label><br>
{/options:app-requested-booth-size}
