If I open Firefox, it shows me Search the web and below of it suggestions of different sites. I want to remove 2 of them. I did right click, but there is no possibility to delete a site (like amazon, hotmail, etc). How can I get rid of sites I don't need and how can I add sites, I'd like to see there?

You'll have to check the Firefox Help documentation: https://support.mozilla.org/en-US/products/firefox/get-started I use Safari and Chrome but I've never used Firefox myself, so I'm unfamiliar with its features..

Is it OK for Mac welfare only to use firefox and not at all safari?

It's ok to use whatever browser you prefer, you don't have to use Safari just because it comes with the macOS.