Why can’t the Time Core be reused?
The Time Core could have been reused, but Akira is so confident that she's finally reached doorstep of the "Perfect Future" that she's just not willing to use it anymore and is ready to allow its destruction.
Does Paradox know Mira survived?
Akira heard Jericho's explanation about Mira's disappearance into a Gene Therapy Clinic when she first crossed paths with her. (Before the events of Chapter 2) Akira was quite surprised to learn that Mira had managed to survive all the way to 2030, but because of what Jericho said, Akira now believes that Mira was flagged for the AVATAR Project and processed at a Blacksite. Due to the discovery of the true nature of the AVATAR Project, fewer and fewer characters are holding out hope for Mira's survival. While Jericho is wholly convinced her adoptive mother is still alive, she's pretty much alone in that belief.
There is simply too much evidence suggesting Mira Mihaka is dead; having perished in either in the Shenyang Clinic or a nearby Blacksite.
If Paradox really is just going to live her life, why did she need to get her teammates killed?
Near the end of her mission, Akira began to see them as a liability. Allowing the team to operate in places she can't see or control them had way too much risk during the final stages of the mission. Akira decided to finish building the Perfect Future by herself so that nobody had the chance to screw it up. She is also highly aware of the fact that Queen Kendra the Great is still alive, and that Kendra will almost certainly be hostile towards anyone known to be harboring the Paradox. Therefore, Akira is trying to keep her footprint in 2035 as small as possible, to avoid starting a last-second fight between herself and Kendra's grandchildren, the Ranginui Twins.
And don't forget, Akira intentionally faked her own defeat and death in
Faith in Chaos. Throwing her team away allowed Akira to kill two birds with one stone: She got rid of a large liability she no longer wanted to have, and she also made the illusion of her own defeat that much more convincing, because the Partogans had the bodies to prove they'd dismantled a "time travel conspiracy."
Will Paradox ever tell them about why the Partogans speak Maori?
Akira is comfortable with XCOM and the Triple Alliance figuring it out on their own. See
Chapter 19: Te reo Māori for more.
How does the info the Levakians on Asalele knowing about Paradox’s actions make the Stormbreakers on Earth, a planet with no extraterrestrial communication outside of ADVENT, mistrust Paradox?
Akira had nearly always antagonized the Gifted Levakians, so they didn't think of her as much more than a malevolent and destructive force. If given the chance, Kaiako's successors would have transmitted a warning to Earth that depicted Akira as a malevolent force and a genuine threat that couldn't be reasoned with.
In previous Cycles, the Gifted Lions of Asalele were able to track Akira to Earth and detect her activity during the 1962 Zudjari Invasion. This prompted the warning message that caused the Stormbreakers to become hostile towards Akira. Now that Asalele has been destroyed, the burden of warning Blake and his team about Akira has fallen onto Manako and Makara Ranginui... two Partogans who are likely to attack Akira on sight due to their familial history with her.
If/when the Triple Alliance learns that XCOM has allied with the Paradox, it'll create tensions between them... possibly even hostilities... especially with the grandchildren of Queen Kendra the Great.
About Paradox’s age, she’s 115 Cycles old. Assuming each Cycle is about the length of time the universe has existed (13.8 billion years), Paradox would objectively be approximately 1.587 trillion years old....
I'm trying to imagine that many candles on a massive cake. I think the cake itself might catch fire.