It's possible to use the user-interface and the icons that I was used to. Or do I need to wait until Valve implements the new customization tool?
It is not possible.
You have to wait, but there are no official sources that states you'll have the possibility to change icons. It is also not clear how much customizable will be the HUD.
If you have suggestions or critiques I invite you to post them to Devs Forum.
You can modify any major resources in DotA2. As far as I know you can at least change the appearance but not the position.
For example: Sounds, Icons, Models, HUDs
The easiest way to get mods/changes to your DotA2 would be downloading mods from other users. A good ressource are modcommunities like Reddit.
Installing those mods is basically done in two steps:
Put the content of the downloaded folder into you DotA2 folder (please read the readme of the mod to see which folder exactly)
Rightclick on your DotA2 in Steam and go to properties-> General -> Set Launch options. There you need to add -override_vpk (More information on Launch Settings here). This will basically say steam to search for custom content to load into the game.
To create your own mods you need to extract DotA2's VPK files with an editor (search for it) to see the structure of files you want to mod. For example you can see that Sandking's Sandstorm ability icon is in a specific folder beneath the root folder (the start folder after extracting). To change this icon you need to recreate the structure to this folder (you only need the folders that lead up to the file) and insert your custom icon.
So for example let's say that the original icon has this path:
Bear in mind that those names are hypothetical because i don't have the actual names in my head
However since modding is not yet officially supported by Valve (but accepted) those modifications can break parts of the game.
PS: I never modded this myself. If my description is false please let me now in the comments.