There are statements in the History of Middle-earth that have bearing on this.
First of all, from the 1937 Silmarillion (end section, paragraph 9), we have Manwe saying the following:
Now all those who have the blood of mortal Men, in whatever part, great or small, are mortal, unless other doom be granted to them...
In the latter QS work (outlined in War of the Jewels) we have no indication of Tolkien modifying this passage (aside from a trivial change from "Manwe" to "Manwe the Elder King" in a part I haven't quoted) so this must therefore have been editorially removed from the published Silmarillion by Christopher Tolkien.
In CT's commentary on the original, he notes that:
It is to be observed that according to the judgement of Manwe Dior Thingol's Heir, son of Beren, was mortal irrespective of the choice of his mother.
Observation 1 - all Half-Elves are therefore mortal-by-default with the exception of Earendil, Elwing and their descendents, who get to choose. This is a special exception (as Manwe says: "
in this matter the power of doom is given to me") and is not available to other Half-Elves. This explains the offspring of Imrazor and Mithrellas remaining mortal and becoming the Lords of Dol Amroth: they didn't have a choice: no "other doom" was granted to them.
In Lord of the Rings and the Akallabeth we have two cases of these descendents, where those descended from Elrond (who chose to be of Elven-kind) were able to make their own choice, whereas those descended from Elros (who chose to be mortal) didn't.
Observation 2 - a decision to be of mortal-kind is irrevocable for your descendents too.
Regarding "elven characteristics", Tolkien mentions in several places that Elves and Men are biologically the same species. Here's a quote from the Athrabeth Finrod ah Andreth (published in Morgoth's Ring) (there are others in Letters):
The existence of Elves: that is of a race of beings closely akin to Men, so closely indeed that they must be regarded as physically (or biologically) simply branches of the
Observation 3 - there are no special physical or biological "elven characteristics" aside from those that may be expected from standard species-variation.
Of course this is difficult to reconcile with statements made elsewhere regarding different growth rates/etc ("if Elves and Men are supposed to be biologically and physically the same species, how you you explain these differences" would probably make a good separate question - I'm not going to enter into speculation here).
Regarding pointed-ears, the only statement by Tolkien on this matter is in a Letter (number 27) intended to provide illustration guidelines for an American publication of the Hobbit:
A round, jovial face; ears only slightly pointed and 'elvish'...
The use of inverted commas on 'elvish', the intended target audience, and Tolkien's own statements that the Hobbit did not (at this time) belong in his mythology, taken together with the "same species" statements, lead us to:
Observation 4: Elves in Tolkien probably don't have pointed ears.
Other Elvish characteristics, such as greater endurance, resistance to illness, etc must come from either one of two sources: (1) normal species variation, as mentioned above, or (2) the immortal spirit rather than physical or biological differences. If (1) then a Half-Elf just inherits normal species variation; if (2) then a Half-Elf, being mortal (see Manwe's statement above), doesn't have them unless exceptional circumstances ("other doom") apply.
I quoted CT's commentary that mentioned Dior, Thingol's Heir and his mortality above, and I'd also mentioned different Elvish growth rates. Looking at the Annals and the Tale of Years for the First Age (published in War of the Jewels) we can pull out a few figures and make some more observations.
Before we do that, let's look at the quote regarding Elvish growth rates (from Laws and Customs among the Eldar (published in Morgoth's Ring)):
The Eldar grew in bodily form slower than Men ..... Not until the fiftieth year did the Eldar attain the stature and shape in which their lives would afterwards endure, and for some a hundred years would pass before they were full-grown.
Now, Earendil's birth date bounced around 500 to 503, Elwing's seems to have settled at 503, and the date of their wedding was given variously as 525, 527 and 530. Either way we're in Human, not Elvish age ranges here.
Also, we know that Earendil was a pure Half-Elf whereas Elwing was a Three-Quarter-Elf, but yet both grew to physical maturity at Human, not Elvish rates.
Observation 5 - any mortal blood means you grow at Mannish rates, not Elvish, and this is irrespective of the relative proportions of mortal versus Elvish blood you have.
So we can put all of this together into a few conclusions:
- The offspring of an Elf and a Man is a Man, in all physical, biological and spiritual concerns
- Half-Elves are actually always Men, not Elves by nature.
- Half-Elves grow at the same rate and mature at the same age as Men.
- Special exception may be made by Manwe, but has only been made once: to Earendil, Elwing and their descendents.
- If a Half-Elf who gets such a special exception chooses to be mortal then all of their descendents are mortal too - they don't get to choose.
- The offspring of a Half-Elf who chooses to be immortal and an Elf is an Elf (hence Elrond's children living 3000-ish years), but can make their own choice. However, the only documented case of this is Elrond's children (Elrond and Elros themselves were born before Earendil and Elwing made their choice) so we can't generalize a rule from this once-off.