Yes, mine came with a tube. The inner diameter of my black-painted tube is 3/4" to accept the cane, which has an outer diameter of 5/8". The included tube is 2.5" long, so it goes 2.5" deep into the ground.
Just about any padlock would work. Find the hardware area of the store and there will be a full rack of locks that will work. I like the big packs of locks all keyed alike--the same key works for all my trailer locks (tongue, side door, back door) and this cane, so when pulling the trailer through the gate (the only reason we need the wide gate) I have the key with me. My locks are Master brand.
Yes, as long as you have space to mount the locking loop. If you're using this to hold two gates together, then the loop would go on one gate, the cane on the other gate. If you're using this to hold one side of the gate closed so the other side can be opened frequently without unlocking it, the loop will need a spot to mount, and that may need to be added. Reach out to a local gate installer/handyman/welder with a photo of your specific application and they'll be able to help.
Yes, the only concern is corrosion between the two different metals. If your aluminum gate is painted where this mounts, then you're all set. If not, use a neoprene tape to insulate the two metals from one another, and use carbon steel screws that are coated. These are a bit over the top, and the corrosion if this is used as-is will likely take quite some time. But, if you're building it to last and last and last for your great-grandkids, check into a trailer shop and they'll get you the fasteners you'll need to join steel to aluminum. Or just paint the aluminum where you're mounting the steel plates.
Yes, this works in a PVC gate as long as it has a sturdy mounting location. Is your PVC gate a white PVC sleeve over a 4x4 wooden or aluminum post? Get the appropriate screws and you're all set.