Will the actions and outcomes that take place on Arkhona be a part of the official w40k lore? And if so, will the outcomes of these battles affect the factions in the lore in any way?

That a very good question. The world of Arkhona is now something official in the universe of 40k, this said we can’t tell if GW will use it in any other story or if it will affect the lore in some manner.

This might happen or not but we have no information to share with you at the moment.