Being in a crouching state reduces the launch speed and with it the stun time and point where it makes you fall down.
What people usually refer to by "crouch canceling", is crouching to have reduced launch power while also ASDIing down, so when they'd normally get popped into the air they instead immediately land due to the ASDI downwards and then the landing animation cancels the stun. You can still get the same effect without being able to crouch and just ASDIing down, but you don't get the reduced knockback from the crouch so it will stop working at lower damages.
You can't cancel the stun on the needles like I mentioned earlier because you can't cause a landing to have that cancel out the stun, but you can still get the reduced launch power from being in a crouching state (obviously you can't though if you are unable to actually crouch at that time).
It doesn't cancel the stun, but it will be reduced since the knockback will be smaller. However, hitting someone who's crouching with more than one needle will have the needles after the first still hit while they're stunned and will break the crouching state and they will be stunned normally after that.
Same thing with Fox's d-air. You can't crouch cancel it because it doesn't have an upwards trajectory and you can't cause a landing off the hit since you never leave the ground, but you can still get reduced stun on the first hit from crouching. The 2nd hit will still connect during that reduced stun time from the 1st though when you're then stunned and no longer crouching, and then the following hits will all act normally.
For the needle->tilt, while the tilt can connect during the needle's stun and they can't actually be crouching when it hits to get the reduced knockback part, they can still ASDI 'cancel' the tilt if the distance they get sent upwards on the 1st frame isn't greater than the distance the ASDI moves them downwards.
If the tilt doesn't send them upwards enough on the first frame to overpower the ASDI down, but the knockback is still strong enough to put them in a tumble they'll just instantly fall over and hit the ground. They'll also be able to instantly tech it when that happens if they time it right.
Needle grab is guaranteed on Jiggs if it's done correctly. Bowser is stunned from a needle for like 10-11 frames even at 0%. If the last needle hits just before landing they don't have time to sidestep or roll before getting grabbed.
