Is my 4 layer board ready for fab or am I about to waste money?

Those pads sitting outside the pour are harmless. Your signals live down in the millivolt range at body frequencies, nowhere near the speeds where a stray copper island causes real problems. An isolated pad just floats along with whatever is near it, wich is roughly what it would do stitched into the pour anyway. If they are test points, either leave them and ignore the warning, or run a thin trace over so the software stops complaining. Same with the notch for the cable clamp, that is a non-issue, just keep any sensitive traces a healthy distance back from the cut edge since routing leaves a rough edge there.

I built something similar for a school project last year and ran the input lines in one tight bundle too, then wondered why one channel showed a copy of another channel in the recording. Spreading them apart a bit and putting a plain ground line between them cleaned it up. No fancy tricks, just space and copper. What spacing are you using between those input lines, or are they basially touching the whole way across?

One thing I'd check before ordering: your analog ground and digital ground. I do board work for a living and on my last biopotential design I tied them togehter at one single point right at the ADC, nowhere else. Splitting the pour and rejoining it at one spot killed most of the digital junk that was showing up on the inputs. Also ask yourself where the electrode reference lead comes in, that wants its own clean path back to the front end, not shared with anything else. Where are you landing that reference on your layout?

One thing I'd double check before ordering is your guard ring or input protection around the electrode connections, since those front ends are high impedance enough that leakage across the board surface can swamp your signal if flux residue sits between input and anything else. I scrubbed my biopotential board with alcohol and a soft brush, then paid extra for the no-clean flux to be removed, and the channel drift I'd been chasing vanished overnight. Ask the fab whether they do a clean before shipping, some do it by default and some don't. Also worth confirming your reference electrode comes in near the middle of the bundle, not at one end, it balances the loop areas.

Update: pulled the input lines apart and dropped a ground trace between each pair, and the bleed-over between channels basically vanished, so that advice paid off. Still fighting a wandering baseline though. When you tie the grounds at one spot, does it matter how close to the ADC that joint sits?