Well the website you looked at has most of the info you need, though finding it can sometimes be a chore. Probably better tutorials out there, just would have to do a search for each particular thing.
For instance, to do checks, you can check out the dialogue stuff. If you are doing a simple check (ie, player has to have at least 50 Repair, or be a male, etc.) then you can just use conditions in their dialogue. Setup a topic, then under conditions pick GetActorValue Repair >= 50. Or GetPCIssix == Male. Or you could add both if it had to be a male with 50 or more repair.
A good part of the website to check up on is : http://geck.gamesas.com/index.php/Category:Functions
Note there are 3 pages there of functions listed. These are often used in scripts and conditions, so it is handy to look through if you are trying to set something specifically as such.
You might also check up on the section on quests, or the tutorial they have for making your own vault, which has a little quest tutorial at the end. It might be enough to show you how to do the basic quest setups, and you can change it as you need. Also checking already made quests is a great way of getting some knowledge from them on how they do things.
For the repair items you could probably also use conditions, depending how you are doing it. Could have two possible outcomes: if player has (for instance) 2 scrap metals, then bring up the repair shop (using GetItemCount as a condition), whereas if they don't, the NPC will say "I need a couple scraps of metal before I can fix anything"). If you want it much more advanced, it may require scripting.
For the quest, you basically need to create a new quest, then use the topics (under that particular quest, usually) to set it up how you want. You could have it start when gameplay begins, then create a topic for the NPC where it progresses the quest. You will often use GetQuestStage and SetQuestStage in these. Also a note, you almost always will use a condition to check "GetIsID" to make sure its the NPC you want saying it (in this case, GetIsID
your npc).
Anyhow, I know this info is a bit strewn about, and doesn't really answer your question on WHERE exactly to read up, but maybe it gives you a starting point. I mostly use the GECK to check out other quests already made and learned from those, posting here when a particular problem crops up. Besides that, just googling GECK tutorials or specific things you need might be worth a shot, then if you hit a specific question ask here. Maybe in the mean time others can suggest better tutorial sites.