All sounds completely normal to me (based on my limited experience of our two white campbells). They also started to lay before we expected them to (but were of potentially varied age when obtained). We also occasionally got a "jelly egg" as we named the ones without shells to begin with - I equated it to them getting everything lined up and working properly.
The size/weight of their eggs gradually increased over the first week or two and took a few months of variability until they settled down to their average (I was sad enough to weigh every egg for about 8 months

) The regularity of laying also took a bit to settle down (and one began laying regularly about a fortnight before the other).
Ducks (can) lay each day as their egg production cycle is 24h whereas in hens it is > 24h and as the start is linked to light levels, I think, as the laying time gets progressively later in the day there comes a point at which the start of the next is delayed and they will miss a day. We did manage to train ours to lay in their house by keeping them shut in until after the time when we were finding the eggs (which helpfully worked out as breakfast time for us), ever since they have had an open house into their enclosed run but still lay in the house most of the time in a nest depression they make in the straw - although oddly, just the one for the pair of them.
The membrane is definitely tougher - might it be something to do with them being aquatic? A good whack or a clean edge - I found hitting the egg with the back of a table knife was better than tapping against a bowl and it either not splitting or spraying egg white everywhere

They are great to eat aren't they! Duck egg sponge cake is amazing too.