Yes, the page is a simple template and you can override it by putting the file template "wishlist.php" inside the "woocommerce" folder of the theme folder.
Yes, you can move the button to another default position or you can also use the shortcode inside your theme code.
Yes, you can change the colors of background, text and border or apply a custom css. You can also use a link or a button for the "Add to wishlist" feature.
Try to regenerate permalinks from Settings -> Permalinks by simply saving them again.
It might be a compatibility problem with the old version of font-awesome, which has been solved with version 2.0.2 of the plugin. Be sure that you are using a plugin version that is greater or equal to 2.0.2. If, after update, you cannot see icons in your theme yet, save again options of YITH WooCommerce Wishlist plugin (that you can find in YIT Plugin -> Wishlist).
This might depend on the fact that your theme overrides plugin templates. Check if the developer of your theme has released a compatibility update with version 2.0 or later of YITH WooCommerce Wishlist. As an alternative you can try the plugin in WordPress default theme to leave out any possible influences by the theme.
Yes, of course you can. To avoid Wishlist page to show product prices, you can hide price column from wishlist table. Go to YIT plugins -> wishlist -> settings and disable option "Show Unit price".
Recently YITH WooCommerce Wishlist has been selected to be included in the "translate.wordpress.org" translate programme. In order to import correctly the plugin strings in the new system, we had to change the text domain from 'yit' to 'yith-woocommerce-wishlist'. Once the plugin is imported into the translate.wordpress.org system, the translations of other languages will be downloadable directly from WordPress, without using any .po and .mo files. Moreover, users will be able to participate in a more direct way to plugin translations, suggesting texts in their languages in the dedicated tab on translate.wordpress.org. During this transition step, .po and .mo files will be used as usual, but in order to be recognized by WordPress, they must have a new nomenclature and be renamed as: yith-woocommerce-wishlist-‹WORDPRESS LOCALE›.po yith-woocommerce-wishlist-‹WORDPRESS LOCALE›.mo If your theme overrides plugin templates, it might happen that they are still using the old textdomain ('yit'), which is no longer used as reference for translation. If you are experiencing problems with translation of your YITH WooCommerce Wishlist and the theme you are using includes wishlist templates (such as add-to-wishlist.php, add-to-wishlist-button.php, wishlist-view,php), you could try to update them with the most recent version included in the plugin (never forget to make a copy of your project before you apply any change). If you want to keep customisations applied by the theme to wishlist templates (still using the old textdomain), then, you should ask theme developers to update custom templates and replace the old textdomain with the most recent one.