Reflections

The critter is almost goose-sized, like a particulary wellgrown shellduck, and in Europe the dabbling ducks where males sport mottled heads are few and generally amongst the smaler species. There is the Gadwall, but his head is rather uniform dull gray... no, thats far less likely this duck has wild ancestors.
But I too feel the streaked look on the head along with the neck ring is strange. Usually it indicates an intersexed duck or a weird state of half eclipse, if we assume natural parent species, but such a duck should be much smaler.

I guess it is a mongrel or intentional cross, with parentage of something pale but marked. There are people that keep Silver Appleyards, Pale Saxony, Golden Cascade or Welsh Harlequins all together with other meat breeds, such all pure white, dark or classic green headed ones, to make merry as they please -- when there is no comercial value or interes in breeder shows is involved and they are seen as pets and ornamentals that is. This kind of funny ducklings can turn out extremly huge.

Geese??? I guess I have to ask about this. An old aquaintance of mine from Flickr times wrote noted papers on the topic hybrid ducks. But I think it is rather unlikely, at the very least I do not believe that they can be crossed into a breed instead of just make a few funny ducks that die one day again without passing on genes before.
Muscovy Ducks and old meat breed Mallard make a great comercial breed called Barbarie for human consumpton, but the buck stops and the duck and drake making the food animals are one a pure mallard and one a pure muscovy each. And better this is, if some numbskull activist frees meat ducks, they at least wont make offspring with each other or any wildlife before the fox gets them.

The two first examples are both Cayuga ducks, the fist probaply an example for either angel wing syndrome or a really poor job of indecisive wing clipping, the poor thing.
That the guy who owns the page for the first duck is a geneticist is not really a proof he might be right. Canada Geese and Mallards sit in the same ponds and can be observed together, and the Cayuga is a common although a tad unsightly breed, especially in case it lacks the dark green full body sheen mandatory in prize drakes. An intentonal crossed melanist gene carrier, it is usually mostly black, at that huge and meaty and quite vocal with a nasal gooselike voice. Proportionally long necks naturally occure in the genus Anas too and some Cayuga breeder support the trait obviously. the proportion recalls a smal Canada Goose -- or a huge Pintail, but it involves neither.
Joern Lehmhus stated in a comment below the second example already that this is a Cayuga. Joern is the most noted german specialist on hybrid ducks, and the Flickr aquaintance I mentioned before.
The third pic I think might be indeed an Egyptian "Goose" with its hybrids. Alopochen are after newest research more related to Tadorna than to real geese, those critters in english named Shel*duck* , in german howerver a "Gans" (= Goose). Barren mallard hybrids with them seem not all that uncommon, especially when the mallard is a domestic bird matching in size. I am sure Dave is right as rain on those halfgrown ducklings but I daubt he will find one of the m leading young of it's own that can be proven -- ducklings of a partner however, well, of course, why not? Tadornes make devoted spouses likely to help raise anything that peels itself out of their lady's eggs, at least until the young bird grows a lot very wrong looking feathers.
So on to pic #4 All I see is a capital hen Mallard, with yellowish patterned mallard baby ducklings and at least one all butter-yellow one promising to become a pure white domestic duck, and a pretty adult Egyptian Goose in their close company. I am not very convinced this bird is dad of any of the short ones, but I don't know the oppinion of the bird. If it was observed leading or warming the ducklings, it may be well it thinks so, however there have been even human men reported thinking they are the fathers of someone, whilst the wife secretly did know better or at least had some good cause to suspect the opposite -- LOL