Hi @tomkormos welcome to Shopify community
Hope your business is going well during these difficult times.
1. In your homepage, I would suggest highlighting a few more collections (Featured Product, Best Seller, and New Arrivals) and keeping some testimonials as social proof as well. Keep in mind that the homepage should be engaging customers, but also not too cluttered which might make your customers bounce off.
2. Your product page is where shoppers can learn more about a product and understand whether it is worth purchasing. By optimizing your product page and adding elements that increase its appeal, you can increase conversions and maximize your sales.
Read more in our blog here to get a complete rundown of how to set up Shopify product pages and what elements you need to set up to get a high-converting product page.
I hope this helps!