I've been doing a lot with jab canceling lately, so I think I can report on it.
1) Link does have to crouch to jab cancel. If you do something quickly enough after it, you won't even really see the crouch come out (because jumping cancels a crouch instantly, even during it's startup frames).
2) EVERYTHING is faster with a jab cancel. Well, most everything anyway. I'm not sure about B-moves because jab-jab-upB isn't a thing in Melee like it is in PM, but nairing, grabbing, and down smashing are all going to be quicker. The key thing you have to remember is that any A move after a jab will count as the next hit in the jab combo, including grab which is really just L+A. C-stick moves don't seem to count for this, but they still will wait for the jab animation to end before they come out. Same with jumps, you won't be able to jump at all until the jab's animation is over (unless of course you crouch).
Also be careful with jab-jab-grab. That's not guaranteed on anybody, but you can use it as a mixup if your opponent keeps DI'ing down and shielding your jab follow-ups. Eventually though, they'll just buffer a spot dodge and poop on your grab, but this is when jab-jab-nair comes in handy because it beats a spot dodge.
/edit: You also don't necessarily have to jump cancel things out of the crouch. I practiced jab canceling by just doing jab-jab-crouch-jab-jab-crouch-repeat over and over again. One of the annoying things about jabbing is that doing the double-jab at nothing actually requires different button timing than hitting someone with your double-jab because of the hitstun. Which is okay I guess, but be warned that accidentally doing only one jab gives you a lot fewer guaranteed options after it.
We need to check the frame data for jab cancelling - the ONLY reason Link would have to crouch is if he has IASA frames that start BEFORE the window to do the next jab stops. If that is not the case, a crouch is 100% unnecessary (and in fact slows your jab cancels). As someone who used to play Brawl Falco (I still do, but he's a backup now), Falcos would jab cancel like this because at the expense of like 3 frames, they could buffer the jab cancel faster (Buffer crouch -> buffer jab out of crouch), but there's no buffering so this doesn't work. And for the record, I do not think Link's jab has this property.
Also, I don't duck when I do jab cancelling. HOWEVER, if it helps you get the timing and you're already basically perfect at it, I don't think you really need to change it.
I also will mix up single and double jab a lot - I think mixing it up is a good idea, since if you always jab->jab-> or jab-> jab -> grab they'll probably just try to CC roll (and so on), but if you just do a single jab -> X you can catch them sometimes. You can also do just a single jab against GnW if you've already got some shield damage and he's not lightshielding to get your shieldstabs in before he rolls (the idea works vs anyone, but his shield sucks so he's a good example of this).
By the way, your frame data is unaltered by jab cancelling - however, you do get to jab them first, which can slow the opponent down and make landing nair/dtilt/dsmash/whatever easier (and for what it's worth, I have used jab -> up+B as an anti-air against floaties - not generally useful, and this may just be a terrible idea [I don't do it much], but you may try messing around with it and seeing what it gets you...).
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Dextrose
bair has the interesting property of having IASA frames before Link touches the ground if you shorthop and don't fastfall (it also autocancels) - so you can do SH bair -> DJ any aerial (fair is not very good for this, I think dair is at best very situational... I usually only use this for another bair or a nair), SH bair -> waveland, and of course SH bair -> grounded stuff (primarily grab, jab, and dsmash). As for following up... read their DI? @
SAUS
can probably answer this better... and for dsmashing right away, I usually just turn around with the control stick and dsmash with the cstick. Also SAUS was the one who told me most of this stuff, so thanks to him for all that (which is why I tagged him since he assuredly knows more about it than I do).