Direct Speech to Indirect Speech

Ye Thuis it grammatical?

Yes.

Ye Thu And can I leave out the conjuction "that"?

I am not personally a big fan of leaving out "that" after "explained", but people do do so. In your case it may be particularly awkward to read as the demonstrative "that" may at first glance appear to be a conjunction.

You s

Ye ThuThe bus conductor explained that that seat was set aside for monks.

Correct.

Ye ThuAnd can I leave out the conjunction "that"?

I don't recommend it because of two "that"s in a row.

CJ

Will I need to change "This" to "the" in the reported speech? Will it be grammatical? Thank you again.

e.g. The bus conductor explained that the seat is set aside for the monks.

Dear CJ, please check up my question and reply me. Thanks a million.

Ye ThuWill I need to change "This" to "the" in the reported speech? Will it be grammatical?

Yes, it is grammatical of course. If the demonstrative force of "this" in the original speech is important, then you should use "this" or "that" in the reported speech ("that" if the seat is now distant; "this" if it is still near). If the demonstrative force is not ver

Ye ThuDear CJ, please check up my question and reply me. Thanks a million.

See GPY's excellent answer.

Note that we are probably at opposite sides of the globe, so I may be sleeping while you are awake. There is no need to post a reminder for me to answer. After I have had my sleep I will get to your question.