What does the reflexive particle "si" add here? The hint gives "to each other", but as the verb is in the singular, that doesn't make sense, does it?
"Čte si" = literally "She reads for/to herself"
There is even an English dialect that uses very similiar "I read me" (I read me a letter).
"Čte si v posteli" without "si" sounds odd.
So is it still a reflexive particle after all? Following the same set of rules (2nd position, jsi si = sis, etc.)?
Yes, it is a reflexive particle. If used without it would not be clear if she reads a book alone or if she is in bed but reads out loud for the entire family.
It isn't, thats why the official translation above says "the bed".
But it would be normally understood it is her bed unless the context implies otherwise.
I suppose that if we added a direct object like 'casopis' or 'knihu', we wouldn't have the reflexive particle?
You would. The reflexive pronoun is there because the subject is "receiving the action". She is reading for herself.
If the pronoun was left out, she would be reading for someone else. It would be weird to leave it out when she's in the bed, but if you added for whom she's reading it, it would be possible. For example: Moje sestřenice čte v posteli pohádky své dceři. My cousin reads fairytales in the bed for her daughter.
You might notice that the English sentence leaves open all these possibe scenarios, whereas the Czech translation chose to specify that she is reading to herself.
We can. Your report was not accepted because of the "the", not because of the "is reading". I will likely add it soon, but I have to investigate something.