a. There is/are either CN (singular) or CN (plural).
b. There is / are either CN (plural) or CN (singular).
c. There is/are either CN (singular) or CN (singular).
d. There is/ are either CN ( plural) or CN (plural).
e. There is/are either UN or UN.
. There is and there are have nothing whatsoever to do with countable and uncountable. The only thing that’s important is whether the noun is singular or plural:
There is a child…
There are children…
There is a tree…
There are trees…
There is some beer…
There is a glass of beer…
There are six bottles of beer…
There is fog…
There are clouds…
There is heavy rain…
There are raindrops…
There is/are either rain or clouds,I’ll go there.
There is/are either rain or cloud,I’ll go there.
There is/are either clouds or rain, I’ll go there.
There is/are either cloud or rain, I’ll go there.
There is/are either beer or bread, I won’t go there.
There is/are either boys or girls, I’ll go there.
There is/are either boy or girl, I’ll go there.
There is/are either boy or girls, I’ll go there.
There is/are either boys or girl, I’ll go there.
Assuming that your question had more to do with using either … or and that all the countable/uncountable stuff was just a smokescreen ;), here are some answers in a format similar to your question:
a. There is either (singular) or (plural).
b. There are either (plural) or (singular).
c. There is either (singular) or (singular).
d. There are either (plural) or (plural).
e. (same as c.)
With there is/are, I would use is/are in accordance with the first noun mentioned.
Keep in mind, when using either, neither or both you might have only one noun:
There are both good and bad reasons for doing that.
There is both a red and a yellow light on my monitor.
There are neither red nor yellow lights my Christmas tree.