I guess embedding then means to show the image directly in the post or comment, without having the need to click a link. Is this correct?

What is Direct Linking?

https://lemmy.fmhy.ml/post/875899

A similar post discussed yesterday. Maybe you’d find some more alternatives there.

Also, do these “image” hosters allow gifs & small videos?

randomly generated seed

What do you mean by this? Usually these hosters offer a link to delete images.