Regarding custom icons, the procedure to add them is very easy.
They are stored within Enpass as 200x200 png files. In earlier versions, you had to convert the Icons to this size. in the meanwhile I noticed, that Enpass can do this by itself. You just have to select a square jpg or png and the upload this file (if the format isn't square, sometimes "strange" results will show up, where e.g. only parts of the icon are shown):
Select an entry and go to edit mode.
Click on the icon and see the dialogue "choose icon"
In the headline of this dialogue you will find a "+" sign on the upper right side.
if you click onto the "+" you can choose a file to be uploaded - search the file in your file system and "open" it.
Afterwards you will be able to select the new icon in the custom icon section
The Favicon function isn't implemented yet - it was part of some beta versions, but didn't find its way to the product version.