About hyperparameters. It see that the format is exactly same (for this Kernel). P is basically tau*I, which is second hyperparameter in my code. You can basically multiply the Kernel matrix with sigma_f, so you don't need to specify. I hope my explanation is clear for you. For now, since we both set it to (1,1), there is no worry there then (and you have made sure the gaussian variance parameter too), and it's all good.

For cold start, you don't have to ignore it. When you don't have any data, then the prediction is equal to the prior mean which is 0 in our case (you could specify other mean function, and then it will predict a non-zero value). This is regression based recommendation, which takes care of the cold-start problem.