100% agree with you on both points.

On the first one, the biasing of the test set, my point is, dont worry about it, the bias is minor.

On the second, YES to all you said. You WILL be overfitting otherwise. I like Machine Learning, philosophically this way: it is not optimization. Find something "good enough" and it is more likely your generalizability is safe, rather than find the tippy top optimum....