Is there ever a third gender in any of the flora or fauna of the Earth?

Answer 1

no

Answer 2

In the cardon cactus in Mexico there are some
individuals which are functionally male only, some
female, some both (hermaphrodite), and some
neuter. In addition all can reproduce asexually, but
this does not really constitute another gender.

Answer 3

There are more than three genders (assuming you mean sex and not gender). Here is a sampling of sexual possibilities:
male only; female only; hermaphrodite (bisexual or perfect in plants), whether self-fertilization is possible or not; apomictic (females producing fertile embryos without fertilization); individuals that can switch between male and female. There are also males who mate with males and females with females, exclusively or not.

Answer 4

Some times trisomic individuals are created that are sterile.

In bacteria there are three genotypes hfr, F+ and F-.
Hfr is male to both F+ and F-.
F+ is male to F- but female to F+.
F- is always a female.

In guppy fish you find XX male and XY female.
In sword tail a mature female that has delivered babies can change to breeding male.

Answer 5

Yes there are life forms which have both sexual organs and can reproduce on their own but the term is not asexual.

Answer 6

Yes, beside males, females, and hermaphrodites their are some born sterile. For example sterile caste of bees and wasps.

Answer 7

some plants are both male and female, there are some that switch. snails are both, as well as some other animals.
but not really a third.
oh and there are these salamanders that are all female.

Answer 8

Yes, asexual. Something that reproduces on its own.
Like many single-cell organisms.