Do I HAVE TO submit predictions EVERY week

In the Numerai Tournament Overview (see, it says “You must submit predictions every week to participate in the Numerai Tournament”. But if I don’t submit my prediction for several weeks, are there any serious consequence/penalty (besides hurting the reputation), ?

No, you can skip submitting for weeks / months as you like and there is no penalty. Your stake isn’t adjusted either up or down for weeks that you don’t submit or submit late.

The reputation penalty is enormous and missing even one week will move you down the leaderboard a large amount, but there is no financial penalty for not submitting.