Both are grammatical. Was is more idiomatic, in my view.
As is often the case with tense and aspect in English, different forms are possible, depending on context. If you are looking through a series of photos, and see one taken during your birthday week, you might say That is my birthday week, focussing on the thought that the photo is here and now, or That was my birthday week, taking your memory back to when the photo was taken. But if there is nothing about the context to bring it to the present, I would always use was.
Your friend's rule ("date always takes the present tense") is simply wrong.
Two unrelated points:
1) your friend's rule, as you have stated it, is itself ungrammatical, as date is a countable noun, and needs an article in the singular. Either a date always needs or (more naturally) dates always need.
2) In most contexts "I guess you have submitted your report during 1st to 7th of January" is odd: we don't usually use the present perfect with a specified time that is fully in the past. Again, it is possible to construct contexts in which that does fit, but normally, I would expect the simple past there.