It doesn't have to be dangerous play to be a red just a deliberate foul rather than a genuine attempt to get to the ball which it was again. The initial shirt pull by Allan happened before the ball was played by Robinson which slowed Powell down from getting there. He probably still wouldn't have reached the ball with the pace on it but Allan didnt know that he was just trying to stop him with an illegal shirt pull rather than a genuine tackle. If he slid in in the vicinity of the ball and missed the ref can give the benefit of the doubt and go yellow, but when it's a shirt pull you've removed any benefit of the doubt.
For Williams, i think its fair to call that a head butt as you dont accidentally charge towards your oponent with your head down over any distance. He easily couldve stood up straight and lead with his shoulder or chest if he wanted to barge into Powell as retaliation or used his arms to push him as he got up - which wouldnt risk a red. It was a deliberate act of aggression regardless of how much impact there was on the shoulder vs the head - he chose to go head first and you can't do that. Much like most head butts in football they often aren't that powerful or a genuine attempt to knock their opponent out (this certainly wasnt) but just a petulant act but soon as you use your head in any way it's always been an automatic red card by the letter of the law.
Err on your first point, I'm sorry but you are completely wrong. The only part of the laws of the game where "deliberate" is even mentioned is around handball. There is no mention anywhere else of that word so I'm not sure where you get that from. "Deliberate" fouls are carried out all over the pitch, throughout the game & every game would get abandoned if players were red carded for deliberate fouls.
As I've said, the only instances in which the Stoke player could have been sent off for that penalty foul was if it was deemed dangerous play or if it denied an obvious goal scoring opportunity - that was neither
There is a recent change in guidance that mentions pushing, pulling etc.. still being red cards even if a penalty is awarded but it only applies to denying goal scoring opportunities and not to every foul in the penalty area. A ref can caution a player for a denial of an obvious goal scoring opportunity if there was a genuine attempt for the ball.
If the ref gave the penalty at the initial point of the foul then the ball had too far to go & too many people to possibly block or get to the ball for it to be a goal scoring opportunity. If its given when Powell falls then he was nowhere near the ball so it wasn't a goal scoring opportunity and therefore can't be a red card offence
As a ref I had to sit through numerous mind numbing training sessions & examples showing what was & wasn't a red card for DOGSO under the new guidance & what wasn't and I can tell you with 100% certainty that that one last night wasn't
In fairness with Williams charge you can make a case for a sending off even if it is a weak one.
But what he did would have to be deemed violent conduct (again nothing to do with it being deliberate) or dangerous play & that was neither IMO. I can see how some could deem it violent conduct but for me the way you run at someone is irrelevant & he deliberately made contact with his shoulder & not his head anyway. For me if you deem running at someone as violent conduct then you also have to deem throwing someone to the floor (which is what Powell did) as violent conduct. You can't have one & not the other
The ref made the right decision in my book by cautioning both for adopting an aggressive attitude rather than dismissing both for violent conduct