I want to try answering a couple of stuff, give my two cents and see if I am nuts or not.
Dorne- The reasoning behind the departure of Dorne from the war falls on a few points.
1- There is now no leader. In order for Elleria Sand to take control she and the Sand Snakes murder Doran Martell and his son. This leaves Dorne without an heir. once Elleria is captured and the Sand Snakes killed there is no one to rule. This means that now all the major houses of Dorne must fight, argue and decide who will be the next ruling family; a process that would probably take some time.
2- Even if Dorne decides to continue with Elleria's plans their army must now march overland north to King's Landing through enemy territory. Highgarden and The Stormlands are now in Lannister control. What was supposed to be a ship ride up to and then a siege of King's Landing has now become a long, dangerous march.
3- The Iron Fleet would pose a threat that may make the new leader of Dorne decide to stay home. If the Dornish army marches north then Dorne would be vulnerable to attacks from the sea.
All said and done I think it makes sence that Daenerys would believe Dorne to no longer be an ally.
Littlefinger- I do not think it was poorly done and poorly explained but rather was very subtly brought to the forefront all season long. In all the seasons after the first, none have alluded to season one as strongly as season 7. Here are some examples:
When Tyrion attacks Casterly Rock he quotes Bronn from season one about impregnating the bitch.
When Tyrion contacts Jon Snow he mentions the line about dwarves being bastards to their fathers that he says to Jon in season one.
Nymeria, who we haven't seen since season one.
Arya saying to Nymeria thats not you, a reference to season one when she says thats not me, refering to herself.
The note Sansa wrote from season one.
Jon calling Daenerys Dany and her saying only her brother called her that, from season one.
Dany and Varys discussing all the plans for her and her brother from season one.
Dany mentioning the assassin from season one.
Jamie saying he learned the trick of splitting his army from Robb Stark defeating him at The Battle of Whispering Woods from season One.
Catspaw dagger, which we have not seen since season one.
What does all this mean? If you caught it all it gets you remembering season one. What was the biggest unanswerd mystery from season one? Who sent the assassin to kill Bran Stark. The dagger should bring that to your mind. Now, we know Tyrion did not do it, and we know the dagger once belonged to Lord Baelish. Truth is the only reason we think the dagger ever belonged to Tyrion is because Baelish said so. So technically the only owner we really know for sure is Baelish.
Now, all the sneaking and schemeing going on between Sansa, Arya and Baelish was alittle confusing, but I believe by design. The real key was Bran. When Arya and Sansa are talking Arya tells Sansa about her list. When later they go to see Bran he makes reference to Arya's list even thought he was never told. Now the girls know Bran knows stuff he shouldn't so whatever he tells them they will believe. Look at Baelish's face when Bran tells him what he said to their father when he betrayed him.
Everything was there, it just took that final piece to make it all fit together.
The Littlefinger scene was so painful to watch. I don't get what the dagger was a symbol of or why it was so important. Littlefinger admitted to owning in it season 1 and it ended up in King Robert's possession. It was used to try and kill Bran but Littlefinger wasn't at Winterfell and would've had no idea about the fall and had no clue where the dagger was kept. We know for a fact it was Joffrey who hired the catspaw to kill Bran in an attempt to please King Robert (he had said killing children in that situation would be a mercy).
No, we don't. Joffery is never hinted at having done it in the show. You are thinking of the books, where even there it is never stated as fact but rather a belief of Tyrion and Jamie.
As for the distance, you have to account for the time things take. While it seems like a day on the show King Robert and his entourage probably stayed there about a month. Ned Stark says it would take about a month of travel from King's Landing to Winterfell so I doubt they only stayed a day or two. With Littlefinger's network of spys I believe he could have put the plan into action to try to have Bran killed. It did not even need to succeed, as long as he coulsd blame the Lannisters for it and start a fued between the two houses.