I understand why "query={1}" was inserted, but don't understand why it was put in that exact place of the string and why "GetSearchQuery&next_mode" was deleted.
I feel if I could understand why it would help me figure out how to setup Project Free TV the same way.
The window that you initially added to your favourites was the Search window for 1channel. So, as you tried, and as PegLegTV also demonstrated, you could use the syntax
plugin://plugin.video.1channel/?section=tv&mode=GetSearchQuery&next_mode=Search
to open that window -- but then you would still have needed to emulate typing in your search string and hitting enter in order to return the actual search results. Doable, but awkward and, in this case, not necessary.
The ultimate search query syntax that I shared came from analysing the next step in the search process. As I think I mentioned above, I actually did a search using that search window, and then I checked the Kodi log to see if it said anything useful about how the plugin was implementing that search. It did.
So the syntax is different because we're actually going directly to the next stage (mode) in the search process, bypassing the search window.
That said, the order of the parameters used in the search query probably doesn't matter. You could just as easily have used:
plugin://plugin.video.1channel/?section=tv&mode=Search&query={1}
My xml for Project Free TV looks like this:
<favourite thumb="C:\Users\NAC\AppData\Roaming\Kodi\addons\plugin.video.projectfreetv/icons/Search.png" name="Search">ActivateWindow(10025,"plugin://plugin.video.projectfreetv/?mode=search§ion=shows",return)</favourite>
I'm not sure where to put the "query={1}" so that when I say "search Project Free TV for" it automatically pulls it up. I have figured out how to open the search, but I can't figure out how to make it insert what I want to search for.
You should try to follow the same process. Manually enter a search in your Project Free TV search window, and then check your Kodi log to see what it says. The plugin determines the syntax, not us.