Is Prince Harry still in the running for "Duke of York" after Andrew's death?

Why would Prince Harry want or be concerned with having any royal title since they apparently treated Meghan so horribly and he wants to do his own thing with her? 

Prince Harry has not lost any Inheritance

There is no strict rule as to who gets it.  It’s just been coincidental that in most creations of the title in the past have gone to a second born son who eventually became king, or died without male issue.  

George V got the peerage after the death of his elder brother. 

£u©K if I know. 

There wouldn't be much point in Charles conferring the title on Harry, even assuming Andrew predeceased both of them, since Harry already has a ducal title.  He'd reason that it was best to save it for Prince Louis when William becomes king.

No, I don't think so; how would it go down being introduced as, HRH, Prince Henry, Duke of York, the first gentleman of the United States?

I wasn't aware that there was "a running" for the title. It's up to Charles,If Andrew predeceases Charles, or perhaps William....but if William is king, that would mean the death of Charles and Harry would no longer be the second son of the sitting monarch... William's son, Louis would be.The title would only be available with the death of Andrew, who is much younger than Charles, so it doesn't look likely that Harry will receive that particular title.

No. The title will be available for Prince Louis of Cambridge in due course, unless (and in the unlikely event) Prince Andrew remarries and has a son. It has traditionally gone to the second son of the monarch, but it depends if it is available at the time, so it won't go to the Duke of Sussex. As chance would have it, previous holders have either become king or had no male heirs so the title became available for the present holder, and will do again.