Eris barely has an atmosphere, so it almost certainly does not have storms.
1. Eris is quite small. 2. Eris is very far away!
Current scientific thinking suggests that Eris does not have a gaseous atmosphere. Eris is so cold that its atmosphere is frozen!
Yes, the sun would be a very bright star. The brightness of the sun decreases as the reciprocal of the square of the distance, same as with gravity. Since the current distance to Eris is about 100 AU, this means our sun would be only 1/10,000 as bright. That is still pretty bright, but you should be able to look directly at the sun without squinting from there.
Artemis and Eris do not share a myth, so we can not determine if they liked each other.
No. Eris was only discovered in 2005. Even if a spacecraft was launched for it right then, it would not have gotten there yet. So far there are no missions to Eris.
Eris is in orbit around the sun. It will remain so unless perturbed from its orbit.
Age is relative, but Eris is a personified concept and the daughter of Nyx in most myths. There are some, however, that list Eris as a daughter of Ares. So the answer is "yes and no".
I heard from resources that we are not sure why Eris was called Eris.
There are no planets further than Eris, but there are Dwarf Planets and TNO's (Trans-Neptunian Objects.) Some of which are: Pluto, Eris, Haumea, Makemake, Sedna, Orcus, Quaoar, and Varuna.
No. No spacecraft has gone past Eris, nor are there currently plans to send anything there.
She had so many children, that they do not know how many she had!