Learn English – Is “should” ever used as past tense of “shall”

I have walked downtown every day for a year.

The "perfect" part of "present perfect" means that the action has been completed. You are saying that your action of walking downtown every day for a year is complete (which doesn't mean that you won't keep doing it).

The "present" bit means that the action has been completed in the present. Let's contrast it with the past tense:

I walked downtown every day for a year.

There is no longer a time frame here. This might have happened years ago, for all we know.

As a side note, please refer to Brians's Common Errors on the subject of "everyday".

Both of the past-tense examples sound somewhat archaic, but that is to some extent because the use of shall in the present-tense sentences does also, imo. (The use of present-tense may in the second sentence sounds formal, but not archaic.)

Probably the last person I heard use might and should with these specific meanings was my grandmother, who learned English as a foreign language about 100 years ago (literally). If your questions is whether you should :-) use the words with these meanings, I would say no, as it will simply be confusing. To convey the past-tense sense of these, you might have to come up with workarounds:

When he was at school, he was not allowed to go to the bathroom ...

He thought that they would go to the restaurant.

Hmm, that second one is tricky, but it's the result of substituting the non-archaic will for shall in the present tense.