Pulling data from one sheet to another conditionally

So I have a bunch of different sheets with tables of similar content, that justify exceeded budgets. What I need to do is compile all of those sheets into one document, one on each tab. I want them to update automatically because I don't hate myself.

I tried to import the data from each sheet into a tab but the problem with that is I can't figure out the column names so I would have to change them every time I update. Also, I only need the lines that actually have content in them.

So how would I go about referencing lines conditionally in a different sheet?