They're basically recurring gag characters who show up in the anime and the manga occasionally. They normally don't play a major role in the story. Except in Chapter 146 Keep Our Beaches Clean of the manga which was never animated where it plays a slightly larger role. They seem to appear less in the Remake for some reason.
Their first manga appearance was not in Urusei Yatsura but in the one-shot chapter Katte na Yatsura from 1978. This one-shot is what put Rumiko Takahashi on the map and also led to the serialization of her first long-running series, Urusei Yatsura.
Second is Super-Delicious Golden Special-Reserve Gorgeous After-Care Kid from Planet Fun #28.
This con-artist Superman parody only appears once in Chapter 231 Glittering, Dazzling Friends of Justice of the manga, and Episode 128 Man or Bird? Gokakenran, Champion of Justice! of the OG anime. Other times he's relegated to cameos.
There is an even more blatant Superman parody in Chapter 106 The Great Off-Campus Snack Battle or Episode 46 Lunch is a Battlefield! of the OG anime or Episode 13A of the Remake.
Third is Yuki Daruma or Snowman.
This shapeshifting alien only appears once in Chapter 115 Tales of a Wandering Snowman and Episode 94 of the same name. It can turn into a cute girl who only Ataru can see.
Fourth is Kintaro.
He's supposed to be based on the Kintaro of Japanese folktale except he's an alien. Just like Lum is an alien Oni.
He only appears once in the manga in Chapter 80 Children's Day Fright. Interestingly, he appears quite a few times early on in the OG anime. He even makes cameos in some OPs and EDs despite stopping appearing in the actual anime for a long time.
Fun fact- Kintaro was voiced by Goku's Japanese VA Masako Nozawa whereas Ataru's OG VA was Piccolo's Japanese VA Toshio Furukawa. Nozawa voiced Kintaro about 5 years before voicing Goku in Dragon Ball.
Finally, it's Ten's mother or Lum's aunt.
According to Takahashi, she is Lum's mother's younger sister. Which makes her Lum's maternal aunt. Like most older characters in this series, she's unnamed.
Her first appearance in the manga is the 2-part story Chapter 160-161 My Mom the Firefighter Part 1 and 2 which was adapted in Episode 76 Firefighter Mama Visits! in the OG anime.
What makes her interesting is that her son is a fire-breathing pyromaniac while she is a firefighter.
She has a second story in Chapter 282 Mother's Heart, Child's Heart which was adapted in Episode 171 Appearance after a Long Time! Worries for Mother the Firefighter!! in the OG anime. Both episodes are worth watching.
Considering how Ten barely exists as a character in the Remake I doubt the Remake would adapt more stories about him. That kind of sucks cause even if people hate him he does have some great chapters.
Sadly, I doubt any of these characters will make proper appearances in the Remake. So I suggest watching the original anime episodes or reading the manga chapters about them since they're quite fun.