https://en.m.wikipedia.org/wiki/Temple_name
Assuming this is true
Who were the Han Emperors who had their temple names removed?
How is it that Liu Xie - a puppet to warlords his entire lifetime - had the authority or prestige to do this when there seem to be zero precedent?
Whats the source for the claim?
On your questions three
The plan was by the scholar Cai Yong and approved by the controller Dong Zhuo. Cai Yong's argument was that traditionally there was only meant to be a limited number of tablets in the ancestral temple to seven. The Han ended up with three temples and a lot of sacrifices going on so by removing those Cai Yong deemed unworthy, it restored the rituals to their proper tradition.
While Cai Yong had a long interest in ritual, that the changes also saved resources when the court, thanks to the coalition's blockade, was under finical strain and Dong Zhuo had burnt some of the temples as he retreated Luoyang, may also have helped get it through.
If you want more on this Cai Yong plan, Professor Rafe De Crespigny's commentary on the ZZTJ in To Establish Peace goes into the matter, commentary on Chuping 1: 190 AD segment X note 51 (search worship of ancestors to find it quickly)
Hope this helps