HE and HIS

Interesting question.

I don't think there could be a rule for something like that. I think the biggest thing you'd want to be careful about is starting a lot of sentences with "he" or "his", especially if the sentences are close together. Other than that, it's probably not a problem. If possible, and if it worked, you might be able to replace some of the "he" and "hims" with "the boy" or "the figure" or something similar. Referring to a person in that way wouldn't be as possibly confusing as using "the shadow".

Is this the first chapter of a book? I caution against not using a name in most cases, because readers tend to get impatient about not knowing who the character is. Not saying it can't work, just that there has to be a very compelling reason for this technique. And I agree with Allycat--think of it like you would the first person POV, and how when you start off with too many sentences with 'I/My' it jumps out at the reader.

As for He/the boy/the stranger/etc, I think you should try to stick to one form of address after your opening few lines. So for example, if you introduce the character as 'the boy' and then move into He, try to stick to that form (he) from that point on, rather than switching back and forth between the two. Just MO.