Weird future tense usage

English has no future tense. Will + the plain form of the verb can express the future, but it has other functions as well. One of them is to express predictable or habitual behaviour, and that’s what it’s doing in your examples.

In both cases will is correctly used. In the first example, will is used to indicate that the doing of a kata is typical behaviour. Swan in Practical English Usage (p629) states:

We can use will to talk about typical behaviour. Example: She'll sit talking to herself for hours.

In the second example, the knowing is in the present and the failing is in the future, so there is no problem in using will:

I know now that at some point in the future I will fail.

For your second point, I'm pretty sure the author uses 'will' because it isn't necessary that the person he's talking about has already failed. Saying:

However, a professional also knows that there are times when he fails, his risk calculations are wrong, his abilities fall short; he looks in the mirror and sees an arrogant fool smiling back at him.

implies that having such incidents is regular; that it happens frequently to a professional. Perhaps the author doesn't want to imply that. It isn't necessary, after all, that a professional must have been through such an incident. He wants to show that although it may not have occured till date, there will be such an unfortunate time when he will fail.

I think in the second example you're confusing a time clause with a relative clause. Time clauses use 'when' as a conjunction, in addition to as soon as, while etc. These never contain future tenses(will/shall/be going + infinitive) because the clause itself stands for a specific time. If you use a future tense here, the meaning changes. 'When' on the other hand can begin noun clauses, or as in this case a relative clause. Here the role of the when clause is to provide a description of something, usually a point of time. In those cases the clause can take any tense at all.

Eg: I'll know when he comes in/ I'll know when he'll come in. With the present tense the clause starting with when describes when the action know will take place. With the future tense in place it would just replace any time as an object of 'know', as in I know the exact time when he will come in.

So in your example : there will be times when he will fail, 'when' is a relative conjunction used to describe the noun 'times' and not a time clause as such. For example you can replace the word when with 'at which' in the above sentence and not change the meaning. In fact, when can often replace at which, during which etc in such sentences:

However, a professional also knows that there will be times at which he will fail, his risk calculations will be wrong, his abilities will fall short; he'll look in the mirror and see an arrogant fool smiling back at him. Hope that helps