I side on Yes.
The argument for No, is on episodic memory which is not reliable. But I think this will eventually fall on procedural memory.
Now, it is known that the human brain - regardless of age - has some level of plasticity. That means that the human brain never loses his ability to acquire new skills, the human brain can always change the neural connections and create new habit.
So, I would argue that his multiple revivals would cause the structure of his brain to change, in a similar fashion in which the brain changes by prolonged practice in complex environments.
And since he is doing the same tasks over and over, the nature of this tasks would become mechanical*. And so, he will be able to learn them by practice, not dissimilar to learning to play a musical instrument or learning a particular choreography. There is no need for him to learn the whole thing at once, he may learn just the initial parts and master them, and then move to next situation, etc...
*: once he has decided what the correct course of action is and committed to it, and once he is past any gross factor.
Given that, I would expect that after enough iteration William will be doing the repeated actions out of habit, without putting much thought on the matter. In fact he will not only do them naturally, but also with better accuracy and even develop a sense for the timing needed to execute them.
My question is: It's our mind and memory precise and capable enough to
repeat exactly the same actions and memorize it to make the day repeat
in the same way as the previous one?
I say, yes.
Yet, as side effect he may require assistance to recover old skills. Take for example the case of learning to ride a backwards bike, after it is done, the person has a hard time driving a regular bike, but provided some practice, it is possible to acquire both skills.
Note: Some people say they forget a language when they learn another, but reality is that they only need a little practice to recover any lost vocabulary of their prior language - although this is anecdotal.
About his episodic memory of events prior to the point to which he goes back... he will not be able to recall. And his sanity... honestly, I don't know... but I can imagine him falling to doing some portions of his war routine without noticing, like a tick or a bad habit.