Lotsa text. You're very right about L-canceling, it's relatively simple. For wavedashing, though, a lot of it is preference and try not to overwhelm yourself as you're new to the game. For example, something you can do once you're more comfortable with general movement is dash -> wavedash, aka wavesurfing, for quicker grounded movement. And yeah, you can't wavedash or waveland forwards without going into the teeter animation unless you held forwards.
Foxtrotting isn't that important, but dash dancing is really important as a function of the game. How it's important between characters varies. For Fox/Marth/Falcon, it can be used as a spacing tool. For Falco, a timing mixups between lasers.
JC grabbing is deceptively easy. For crouch canceling, it tends to be really % and spacing-based, so it's hard to explain all at once.
Using running shineturnaround bair isn't necessarily bad, but just recognize you won't always have the time for it. Nair suffices most of the time, and when you need vertical hitboxes, your fair covers that pretty well. Laser tech is just a matter of getting used to, as is getting used to Firebird.
For combos, n/dair, shine, and utilt are his main things, which lasers being how he tries to create openings that let him land those moves. Once you're in the combo is when he gets really interesting.
Not sure what you mean by jab locks, but I think you may mean jab resets (different terminology between games). Because of how the function works in Melee and due to Falco's ground speed, a low laser is his main option. What I like to do is follow up where they're gonna have to tech with a laser just in case they missed the tech. It's pretty nice.
Falco's throw options are tricky. The biggest thing with them is that grabbing makes it so your opponent wants to shield less a lot of the time, meaning you get easier combo starters. Against spacies, you can get bthrow regrabs if they DI in, which is really useful. Uthrow is generally what you wanna use, though, because if you read their DI a bit you can shine them for it. On floatier characters (marth/peach/puff?) you can uthrow fair sometimes. Other than that, fthrow if it will put them off the ledge. I personally enjoy Falco uthrow a lot and then prefer to just take stage positioning. Lemme link a few videos real quick.
https://www.youtube.com/watch?v=wpxR9WSUvwg&list=PLoU3TQBakHOp0LFIjbrfUA8ibLMx6dfWV SSBM-Tutorial's full Falco playlist
https://www.youtube.com/watch?v=uRa7249dBWk food for thought for now until you're more comfortable, but this is important to keep in the back of your mind.