Question about ASUS ROG Strix LC 360 RGB White Edition Complete water cooling

Yes, since about mid-2021 everything has been adjusted so that it works perfectly. I use the cooler with an LGA 1700 (i9-12900K). The cooler is not only visually impressive - it also cools really well (the i9-1200K is notorious for its heat). I would still recommend the LC II...

No, only newer variants named "LC II", i.e. II for 'second' generation officially fit.