I'll list what I've dug up on the matter in the past. Though keep in mind these books are D20 and not Forgotten Realms, so it's not completely cannon. Still a good guideline, I think.
Complete Guide to Fey, p 10-11 wrote:
There are five ways that new fey may come into existence.
These methods are:
1. They (male or female) may mate with mortals, drawing on
their unbound life energies to create progeny. Fey created in
this way show no physical signs of their mortal parent,
though a bit of the mortal’s emotional tendencies and attitudes
will carry over. The mortal supplies the clay and the
fey supplies the design. Fey born of a human mother will
always be the same type of creature as the father.
Children of the Fey, p 2 wrote:
The feyborn are the product of mortal parents
whose blood contains some tinge of fey magic.
Many are born to mortal parents, although their
ancestry may be tinged by a great-grandfather
cavorting with a dryad, but some are the result
of a powerful blessing from a fey creature of
great power while the child is still in the womb.
The favor of a fairy is a powerful thing, and
their good will towards one who is not yet born
can have a powerful effect on their blood and
destiny.
The feyborn are marked with strangeness,
right from their moment of birth. There is
something strange and magical about them even
when they lie in the cradle, their mis-matched
eyes changing color with the shift of the winds.
As they grow up, they exhibit an even stronger
affinity with fey magic, possessing a natural
way with the plants and animals of the woods
and occasionally exhibiting some outward flash
of fey magic.
Feyborn are more at home in the wilds of
their fairy ancestors than large cities. Many
suffer torment and ostracism at the hands of
superstitious villagers that fear their fey nature,
while others find the touch of fey-blood a
blessing as they grow into maturity. From a
young age, they exhibit a strong connection
with the natural world and magic, and many use
their skills to play practical jokes and tricks on
those that surround them.
According to the last book, "Feyborn" is the more general term of fey+nonfey parents.
As to the two questions, I'll answer them with my opinion on the matter. Not that I know for sure if my opinions are following what little Forgotten Realms cannon lore there is on the matter or not though.
According to the first book, on the first way to "create a fey", it lists that fey born to a non fey mother, is always the same type of creature as the father. And when a non fey male mates with a fey female, it is a fey. It's somewhat conflicting, since according to that they can never really be any half-fey. Though I would say that the race of the offspring from a fey+nonfey coupling is dependant on the parents, since some fey seem to be able to "choose" how much of themselves to give over. Making either a fey child, with little signs of the mortal parent, a feytouched or a child of the same race as the parent, in this case a moonelf or other kind of elf.
If it's not fey, it would say it still carry part of the bloodline from the fey parent, though not showing many symptoms of it. Sory of like the cases where seemingly "normal" parents give birth to an Aasimar or a Tiefling. I.E you can have two seemingly normal elves, where one of them has a fey grandfather or great-grandfather or whatever, then ends up giving birth to a feytouched child. I'd say go with the same general guidelines as you would with a tiefling or aasimar's heritage.
Like the first way to create fey lists, FEY born from an unity between mortal and fey look like their fey parent, but take on the emotional tendencies of the mortal parent. It doesn't list any other outcomes spesificly, so I wouldn't know if only fey are born by that unity, or not.
I'd say it's likely they can create an elf or a feytouched, but that some characteristics would definatly carry on from the fey. Such as the unnatural grace (and the charisma + charm boost that comes with it), and maybe some personality quirks. But overall resembling the elf more.
In example, human+human coupling often ends up with the kid looking like either of the parents, not too common to carry alot of traits from both since some genes are stronger than others.
The Children of the Fey book, lists the same general type of racial traits as a feytouched, except they call it a feyborn. So I would guess a feytouched is the result of an elf+fey, where feyborn is the general term for fey+nonfey. I'll list them below.
Children of the Fey, p 4 wrote:
Feyborn Racial Traits
· +2 bonus to Charisma, -2 penalty to
Constitution. Feyborn possess powerful
personalities and a strong sense of selfawareness,
but they are frailer and weaker than
normal humans.
· Medium: As Medium-size creatures,
Feyborn have no special bonuses or penalties
due to their size.
· Feyborn base land speed is 30 feet.
· Low-Light Vision: Feyborn can see
twice as far as a human in starlight, moonlight
and similar conditions of poor illumination. He
retains the ability to distinguish color and detail
under these conditions.
· Spell-Like abilities: A feyborn with a
Charisma score of at least 11 may choose one
of the following abilities: 1/day – charm
person, 1/day – disguise self, 1/day – entangle
or 1/day – faerie fire. Caster level 1st; save DC
10 + feyborn’s Charisma modifier + spell level.
Once chosen, this ability cannot be changed.
See the spell descriptions for more details.
· Add +1 to the Difficulty Class for all
saving throws against enchantment spells cast
by the feyborn. Their innate connection to fey
magic gives them a talent for beguiling others.
This adjustment stacks with those from similar
effects, such as the Spell Focus or Fey Sorcery
feat.
· Automatic Languages: Common. Bonus
Languages: Draconic, Elven, Gnome, Sylvan
and Goblin. Feyborn learn the languages of
many creatures that inhabit their forests.
· Favored Class: Bard. A multiclass
feyborn’s bard levels to not count when
determining whether he takes an experience
point penalty.