My site loading speed is really slow, especially on mobile. How do I improve the speed?

I want people to see a larger image when they click on the product image. You can visit Etsy for reference

How to show categories on the left side when you open a particular product page so that people can browse different categories right from that page instead of going to the shop page again. And I have separate pages for each category; how do I add the categories filter on the left side? I have separate pages for each category because I have a shop-by-category section on my home page, and I want to link that to those particular categories.

Keeping everything between the vertical grid lines leaves a lot of space on both sides and does not look appealing. Is there any other way to ensure that websites look good on all devices?