is this algebra's script?
You are the one who got that script somewhere, and didn't give that link, only a short part of the script in a picture.
So you have to say whether this is Modern Algebra's script, perhaps by reading the header of the script where it's name is listed.
I'm not sure where or how to input my data for the quests I'm wanting to show up in the quest log
and does it use switches to tell it when to show quest data and when it is finished cause it seems to me it would be that simple
I mean I don't know much about scripting but it would seem after you have the log you should just be able to use switches inside events to tell it when to
show the quests and when to show the completed quest text
All texts needs to be put into the script, that includes the texts for script description. If that is Algebra's script, then he included examples and a very good description in the comments of his script, you have to read that part (the manual part) of the script.
And no, it is impossible to tell a quest log with switches when quests are complete and what texts to display - theoretically it might be possible, but that would require a lot more scripting knowledge to tell the script which switches to use.
So your last assumption is completely wrong - you need to know script calls to change the status of that journal's scripts, and Algebra used script calls because that solution is easier than programming the script for switches. Because that "programming for switches" could only be done by the game developer who defines the quests, not before that by the scripter.