One other thought...where's the tank located? Is it near a window or some other light source that could be causing an algae bloom? I'm a fan of live plants to help stabilize a tank. In something that small you could get some marimo moss balls or susswassertang/subwasstertang. Those would do ok without any light in the tank at all. Where are you located? If in Texas, DM me and I'd be happy to mail you some extra plants.
You probably already know this, but keeping that 3 gallon tank healthy will be tougher than a 10 or 20 gallon tank. You should kill the light while you get that thing cycled. You can add a sponge filter as a secondary filter and it will give plenty of surface area for that little tank. You could also just buy some plastic pot scrubbers and cram them into your existing filter. I bet the flow on your filter is fine, but it just needs some media to build up bacteria. Also, don't worry about any RO filter. Just use tap water and dechlorinate with Prime or something.
I think @Updawg is probably right that you have two problems. Think of something like the diagram below. On this sink, the chrome tailpiece sits inside the white PVC extension. Even if the connection is loose, most of the time water will just flow straight down and there's no problem. But if the drain is clogged water could back up past the tailpiece/PVC joint and that's when you could get a major leak.
I haven't watched the whole thing yet, but I'm a bit underwhelmed by Talarico in the first 30 minutes. He's serving a lot of canned data points and anecdotes and I wish he'd do more to get to practical ideas. I still like the guy and now I'm thinking the primary with Crockett will be a good test to sharpen the messaging.