At very least, keep for arena 

As in, Keep Khatun for Arena? Is running both these guys make sense ever? Do the buffs not stack? Fire Knight giving me fits over here. 

the buffs do not stack. the only buff that a champion can have multiple copies of is the continuous heal buff.

generally speaking, you won't ever have call to run both khatun and apothecary in the same team. however, as krama said, khatun will be far more useful than apothecary in arena, so she's worth building for that alone. even if that weren't the case, i would advise against getting rid of any epic or legendary champions unless you already have them.

Another thing, High Khatun will be of big help sometimes, more than Apo, like in force affinity maps, or where lowering the turn meter is allowed (like fire knight for example). Plus she can decrease speed on enemies and certain bosses. She could be useful for you in Iron Twins (up to a certain level, but still).

And she'll be of good help in your Barbarian faction also. There's nothing wrong with making her 60, but you could decide she performs well enough at 50. That depends on your account progression i guess. But for a good while, she can be a great addition to your roster. Getting Arbiter will take some time still, so if i were you, i'd level her up :P

Apo doesnt have speed aura , HK doesnt have heal ... you dont do anything , you use them both in their required situations .

Another vote to keeping both.  They will have a use in a lot of content as you move forward.

If it were me, I'd probably move all of my speed gear over to HK and make her my speed lead in Arena, and then outfit Apo differently depending on where else I need him.  He no longer needs to be the fastest