How quick is worldwide communication, on average?
That depends on who you are! Great Houses, and many High Houses, the very wealthy, and larger businesses will have telephones and so can communicate that way, pretty quickly. There’s a postal service, but whilst that can also be quick locally it can take several days over longer distances.
Although there are telepaths, most only have a fairly short range so that’s not much practical use; telepaths may be used in conjunction with phones to reach places with no phone, or to be more mobile. Traders have developed telepathy over distance which gives them a distinct advantage in trading both products and information. They keep this ability pretty much secret though.
Here’s an extract from Strand of Faith, where Gabriel is talking with Simeon, who has brought a message from the local Settler community:
Gabriel understood. “Let me help. I should think it started when your family came to the Christmas service at the Abbey and your uncle, or possibly your aunt, talked to Leonie. Am I right?”
“It was my aunt. And then we all went home and there was, there was a Calling.”
Most people knew that Settlers were Trader families who had decided to leave the traveling life and stay in one place. Very few knew that this was rarely their main motivation. Whilst other Gifts were rare amongst Trader people, Trader women were almost all telepathic. By placing their strongest telepaths in key towns on their major routes, and in each caravan, they had established an extensive communications network. A Calling directly linked one or more community or caravan leaders. It took a great deal of energy; the most powerful telepath in a group would link to the others for additional power, but they would also link to, and draw energy from, other non-telepathic members of their community. Hardly anyone outside the Trader community and caravans knew anything at all about their ability to communicate like this. Gabriel's knowledge had been acquired many years ago in circumstances he chose not to think about.