Unfortunately, this is not possible with the way this mod communicates with Discord. Webhooks can only be sent to Discord. If you really need that feature, check out DiscordMT (https://content.minetest.net/packages/archfan7411/discordmt/), which comes at the cost of a Discord bot and is therefore a lot harder to set up and operate, as you need to have a seperate Python program running in parallel to your Minetest server.
MineClone support means the public inventory is displayed correctly, as this needs to be implemented additionally because MineClone uses a themed Formspec. Also, there is no integration in the MineClone inventory GUI, as it doesn't support the addition of new tabs / buttons, at least as far as I know.
The mod is meant to be used with the command, but if you want to add a block, you can do this on your own and use the pubinv.open(playername) API, which first needs to be enabled by removing the "local" in front of the pubinv table definition in init.lua (highlighted in the code!).