Is it possible to say, for example, "Er/sie werde den Ball werfen." (He/She will throw the ball)?
If so, what is the difference between that and the regular "Er/sie/ wird den Ball werfen."?
"werde" in 3rd person singular is Kunjunktiv I. This form of verb is nearly only used for inderect speech.
"Er sagt, er werde den Ball werfen."
Yes, you are right, Jussel11. ...Sorry, I seem to be at war with the subjunctive. : )
Milo47, for further information please have a look at this site: https://deutsch.lingolia.com/de/grammatik/verben/konjunktiv
Should you always use Konjunktiv I for indirect speech? Is it wrong to say “Er sagt, er wird den Ball werfen”?
Also, what do you mean by “nearly only”? What other cases besides indirect speech could you use this form for?
No, it is not wrong. Many Germans do not use the Konjunktiv I, where it would be necessary. It is hard work for German teachers to say the pupils use it at least in an analysis. Even in 12th grade one month before final exams in a Gymnasium ("university prep-school")...
So of course it is allowed. Nearly everyone would say it like you. Or even "Er sagt, er wirft den Ball.", when it is clear that future is meant.
But sometimes (still) Konjunktiv I is used. For example in a newspaper article (of a good newspaper) or in radio- or tv-news (for example Tagesschau). Donald Trump kündigte an, er werde die Zölle erhöhen.