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3- People are going to suggest squats, I hate squats. In high school I was doing them bad and ended up emptying both sides of the bar on the floor and it freaked me out. I’m not very comfortable doing them, so I like to avoid. Also, I strongly prefer to stick with machines over free weights.
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Dids, free weights are far superior to machines, but I can understand your reluctance to do more intimidating exercises like bench press or squat where you need a spotter/there is a perceived risk of injury.
I'd suggest trying out free weights for easier exercises and see how you like it. If you try them, I think you will find that they are more enjoyable, and then you might be willing to try more intimidating free weight exercises like the squat and bench press.
One exercise that I would highly reccomend is the standing overhead press using a barbell:
This is a great shoulder exercise and also hits the triceps. But it also improves your balance and requires you to stabilize your core. Moreover, it will give you some experience pushing free weights (ie bench press) and standing with weight (ie squats). And since you will probably be using pretty light weight (just start out with the 45 lb bar and see how it feels), you shouldn't feel too intimidated.
Hell, even do bicep curls with free weights. That's pretty much the easiest free weight exercise there is. There's many other great free weight exercises that you can do that are not too challenging if you want more suggestions.
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4- So what do we think of my plan? Is anything painfully misplaced? What should I add, what should I drop? My gym is pretty damn nice (LA Fitness) so if there's something you suggest, they've probably got it.
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I'd turn your "chest and arms" day into chest and triceps day, and your back day into back biceps day, and do abs on your leg day. The philosophy behind doing triceps on your chest day is that most chest exercises also hit your triceps to some extent, so if you also do triceps that day you will hit them fully and give them a full week to recover before working them again. Same reasoning for doing back the same day as biceps.
Oh, and as far as diet goes, from glancing at your cooking threads it seems you eat a lot of fish and vegetables, which is fantastic. As far as breakfast goes, I highly recommend oatmeal. It's a much better source of fiber than wheat bread, which is probably processed and enriched with bad stuff.