Back in college I listened to Chinese music almost exclusively for a few years, but what I find to my liking is not everyone's cup of tea. Some of these are main themes/sub themes (slow, ballad-ish, soft rock songs) from a lot of Chinese TV dramas and movies that I used to binge watch 20-40 eps in a week when I had a lot of free time. I also can't tell you what most of these titles mean because I can't read Chinese, but I can tell you who it's by :P
A lot of these are sung by actors which I would not consider singing their strong point because almost everyone in the HK entertainment industry that acts attempts to sing and vice versa, so it's probably auto tuned out the ass and there are very few people that are good in both areas...but hey I like how the songs sound and it's nice I don't need to read lyrics to understand the song. There are very few female singers I would consider legitimately good singers in the Chinese music industry (I would consider GEM the best by far out of this current generation), but here's some songs I like. Some of these are sung by male singers as well and almost all of these are Cantonese:
Joey Yung - 連續劇 (Joey Yung is a singer, not an actress)
Niki Chow - 心變
Raymond Lam - 幼稚完
Raymond Lam & Eva Huang - Promise (this is from the movie, The Sorcerer and the White Snake. This song is in Mandarin)
Alfred Hui - 我的離開也是愛
Kary Ng - 座右銘
Kary Ng - 明知做戲
Alex Fong & Stephy Tang - 十分.愛
Elanne Kong - Hand Print
GEM - 有心人 (this is a cover of a classic song)
GEM - 喜歡你 (another cover of a classic song)
GEM - Tornado (this is also a cover of a famous Jay Chou song, in Taiwanese)
Can't help you with the two videos you linked though, I have no idea who they are...