I forgot to include a few last sentences.

When reporting the following sentences:
1) "Have you done your homework yet"
should I use already in reported speech?
She asked me if I had already done my homework/or had done my homework yet.

2)"She arrived last Saturday". She said she had arrived the Saturday before/the previous Saturday (are they both possible?)

3) "Is your birthday next month?" She asked me if my birthday was the following month/the next month/ the month after /afterwards? (Which are possible??)

tomorrow: the following day, the next day, the day after (is a mistake because after is a preposion??)

1. Sorry, but I do not understand this statement: "should I use already in reported speech?"

2. Yes.

3. All

Sra

P.S. After is both an adverb and a preposition and afterwards is an adverb

To answer your questions:

1) When reporting the sentence "Have you done your homework yet?", you can choose to include "already" in reported speech, depending on the intended meaning. If you want to convey the aspect of completion before the time of asking, you can use "already" in reported speech. For example, "She asked me if I had already done my homework." However, if you prefer not to use "already", you can phrase it as "She asked me if I had done my homework yet."

2) When reporting the sentence "She arrived last Saturday," you have two options to refer to the previous Saturday: "the Saturday before" or "the previous Saturday." Both options are grammatically correct and can be used interchangeably.

3) When reporting the question "Is your birthday next month?", you have several possibilities to refer to the upcoming month: "the following month," "the next month," "the month after," or "afterwards." All of these options are valid and can be used depending on your preference.

As for your comment about "tomorrow" and its substitutes, you are correct that "after" is a preposition and not appropriate to use in this context. The correct substitutes for "tomorrow" would be "the following day," "the next day," or "the day after." These phrases can be used interchangeably and convey the same meaning as "tomorrow."

Remember, the choice of words may vary depending on the context or personal style, so you can select the option that fits your intended meaning or sounds more natural to you.