Hello,
answering your questions:
The main menu background image can be customised, but you need to be an osu!supporter to do so, which is paid.
Currently, the background image is featured artwork that the public has made for Christmas. An update will come soon that reverts this to the default background, which is usually just patterns.
For Beatmap backgrounds, there are a couple ways to do this, but it isn't possible in skinning unless you have supporter.
1: (works inside gameplay only) At the start of a song, when it's loading or in it's intro, move your cursor down to the "visual setttings" panel and fully max out the background dim. This will make the background completely black while you play. Its also available in the pause screen and settings panel from the main menu. (doing this from settings panel sets it for all beatmaps. and all new beat maps for now on. basically a master control)
2: Manually remove backgrounds in the "songs" folder within osu!s file directory. To get there click "show skins folder" under "skins" in the options panel (main menu), go back out of that folder and the songs folder should be there. Delete the background images or replace them with your own here.
3: Use an application that removes backgrounds or changes them
There are a couple of user-made tools that change backgrounds... Here's a good one:
https://osu.ppy.sh/forum/t/424666The "Key Inputs" shown at the side of the screen show which keys or mouse buttons the player is pressing. It's just an interesting thing for trivial info.
In osu!:
M1 / M2 = Mouse buttons 1 & 2 (left and right click)
K1 / K2 = Keyboard buttons 1 & 2 (defaults are "z" and "x" but you can customise them. If you're new to this, you can click on the keyboard instead of mouse for faster clicking)
In catch!:
The buttons change in catch.
The top two represent left and right keys, and the third represents the dash key (shift)(used for faster movement)
Bottom is greyed since it isn't used.
See it in action by replaying some persons play, its most interesting watching a person play the hardest ranked map you have.
(click a score in the global leaderboard, press watch replay (or whatever your skin says)
Just ask if you have any more questions