1. Actually, page speed is depends on many factors, such as internet speed, server speed, scripts loaded, images optimize and etc.You can try to disable all plugin except the required plugin and try to optimize your images.
2. May I know do you use shopping cart on your website? If not, you can simply disable WooCommerce plugin and Shopping Cart icon will disappear from menu.
3. Can you provide me the page url that you referring to, i will check it directly about this thing.
4. Did you mean is to add custom style on those page?
And thanks for your kind words and suggestion, very appreciate it. We will considering about this thing especially for gallery.