Recent events in Game of Thrones have made me question the size of the Narrow Sea. Are there any indications in the book about how much time it takes to get from one side to the other? Or are there any advances in naval technology that make the journey significantly faster now than in the beginning of the series? Crossing seemed to be a big thing back then, whereas now it seems you can make it there and back to Essos in two days or so... I am referring to the travels of Varys (Dorne-Meereen), Arya Stark (Braavos-The Twins) and Yara Greyjoy (Pyke-Pentos).
All three examples you provide can be explained by asynchronous storytelling.
Asynchronous storytelling is a common tool in Game of Thrones and explains most of the timing discrepancies that we see throughout the show.
Varys: (Sourced from my answer to this question)
We can assume that Varys' meeting in Dorne (earlier that episode) occurred well before the final scene showing the fleet leave Meereen.
Arya really has not interacted with a main character from Westeros since she traveled to Braavos. As such, it's difficult to pin down exactly what events in Westeros correspond with her storyline.
Because of this, it is reasonable to use Occam's Razor to pick the simplest explanation. Which answer takes the fewest mental gymnastics?
- The narrow sea is magically shrinking
- A society that doesn't seem to ever advance has invented a new form of travel
- The show runners decided that it would be boring to show months of travel and so just didn't show it.
The answer is 3.
See the section on Arya, all of this also applies. The Greyjoy storyline has been split from the other storylines, and so it's difficult to determine how much time has passed.
In addition, there is a quote from the Producer answering this one:
(Interviewer) Another time-related question: It feels like we’re jumping between storylines that have very vastly different lengths of time passing between each scene?
(Bryan Cogman) The timelines between the various storylines don’t necessarily line up within a given episode. For instance, the “Northern Tour” Jon and Sansa embark on would probably take a couple weeks, but Arya’s storyline over the past few episodes only spans a few days. We realized a while ago that if we tied ourselves in knots trying to make all the “story days” line up between all the characters the momentum would suffer.