Can someone recomend me games for Nintendo DS? or something like Osu! and if you can give me a short summary. Thank you.

I had a Ds for years i can recommend a few things

Elite Beat Agents:
its exactly osu, you cant put in your own songs but portable osu if you want to import a more japanese version then Osu! Tatakae! Ouendan

Lunar Knights:
this game is a pretty amazing action rpg there are 2 playable characters and a fairly deep day/night/weather system

Shin Megami Tensei Devil survivor 1 and 2:
Really fun tactical rpgs with a great story

Luminous Arc 1,2 and maybe 3:
Fantastic tactical rpgs and my favorite series on ds by far, ive never played the third one so i cant say anything about it but the first 2 have great stories, great soundtracks and awesome characters.

well it's not like osu! but its one of the best games in ds :
- professor layton series ( alot of puzzles and enigmas that u need to solve )
-pheonix wright series ( you are a lawyer and you need to identify the lies and present evidences.. it may sound stupid or vague but its awesome once you play it )
disgaea ( its a tactical game .. really fun and with a nice scenario )
the world ends with you ( this one is a bit difficult to describe but its awesome XD )

1.all of the pokemon games...ALL OF THEM!!
2.spectrobes
3.mario partners in time, or bowsers inside story