Another idea is that is he got a lot of information from Felassan. He says to the Inquisitor that his agent (that we know from Masked Empire is Felassan) had the task of recovering the control of the eluvians from Briala. That would have been his mission at the end but he was around for 20 years at least prior to the events in DAI. That would have given him plenty of time to find out the current situation in southern Thedas and pass the information on to Solas via the Fade. When he first met Briala she was running away from the Orlesian Court and trying to find the Dalish. Whilst Felassan may have genuinely thought she would be better off returning to Celene's side, it does strike me that in encouraging her to do so, he was acquiring himself a perfect agent inside the Orlesian Court. It is confirmed in Masked Empire that Briala certainly did pass on information to him, because he passed it on to the Dalish clan we encounter in the book.
Felassan is a dreamer so can enter the Fade at will. So sometime between encountering Imshael and reaching the control point for the eluvians, he contacted Solas and told him what was going on. He was ordered to take control himself or at least get the means to recover control later. However, Felassan decided to disobey orders and stopped Briala from telling him the password, so Fen'Harel killed him. According to Cole this was not for the crime of disloyalty but for seeing Briala and her elves as People.
I assume that Solas could tell from the Fade when his orb was nearing full power and this is why he probably woke Felassan from uthenera and sent him out on his fact finding mission. Even if Felassan didn't know exactly what Solas was planning when he awoke, he certainly knew he was going to do so because he hinted as much to Imshael to get him to back off and leave his party alone. Then when Solas did wake up, he probably went into Ferelden first, down south near Ostagar and as well as listening to the spirits there, he also visited Flemeth's old hut.
The rest of his information he probably did get from the Fade, since he mentions about a Qunari cook in one of his tales and I doubt he was ever in Par Vollen. We know from Feynriel that there seems no limit to the range of a dreamer when contacting other people's minds.