[Legolas]

I am not aware that Elros displayed any ability I mentioned - nor that any Man shared them. This are specific Elvish traits, gifts of their race.

How would you be? We're told very little about Elros. Any apparent difference would certainly be explainable - his genotype may be from the same parents, but his phentotype still may be different, just as brothers of any sort can be and usually are different. The influence of his ancestry does not disappear because he has chosen mortality. Being of elvish descent I would expect Elros to exhibit flashes of Elvishness. Why wouldn't he? It is precedent. His extra long life is the obvious example. There also seems to be traces of Elvish strength and 'wisdom' or 'cunning' in some of his descendents (evident in Aragorn). This also makes Aragorn's childhood in Rivendell understandable, or at least easier on Aragorn. Also, see below for the Imrahil-Legolas point.

Why? Is there any sign he had them before he made the choice?

We're given no reason to believe that they magically appear when he chooses to be immortal. To say that they did would be more speculative, and goes against what we see.

As dilute as Imrahil's Elvish strain was, Legolas still recognizes it instantly:

At length they came to the Prince Imrahil, and Legolas looked at him and bowed low; for he saw that here indeed was one who had elven-blood in his veins. ‘Hail, lord!’ he said. ‘It is long since the people of Nimrodel left the woodlands of Lórien, and yet still one may see that not all sailed from Amroth’s haven west over water.’

Imrahil's only elven ancestor was twenty-three generations ago. Why then do you think Elros and Elrond would not show the "elven-blood in [their] veins"?

I would call this a false comparison. Gimli didn't make any choice (as Elrond did); he was a guest in the elves' home. He would die there, to the manner of his kin; Elrond would live to the end of the world, as elves do.

The point was directed solely at Rhod's comment - you do not have to become an elf to be accepted into elven society. The fact that Elrond is accepted has nothing to do with "being a full Elf."

What sets apart Half-Elven from Elves from Men among them (in genotypes, or by whatever criteria you consider relevant)?

The mixture of Elven and human traits? I'm not sure what else you're looking for.