establish a platform discussing history of Tiennaman square or Uyghurs without strictly adhering to government set guidelines, then they will likely be prosecuted.
Tienanmen square has a 600 year history. You're referring to one event, which is censored. But even that doesn't cover the portion that is relevant to the history of Tiennaman, no part of the protests is censored. Uighur history also doesn't have any censors.
It is true that you have been able to identify one censor in your two topics (albeit with inaccurate wording). It's also a particularly sensitive topic with strong disinformation campaigns targetting it. In 2020, many states worldwide issued censors on COVID and vaccine related topics for similar reasons.
It's weird to me that this particular law was the one the colour revolutionaries rallied behind.
A Hong Kong resident confessed to having committed a murder on Taiwan. China extradites people summoned for court or with arrest warrants issued by the Taipei rebel government to Taiwan as long as it's for non-political offences. So they would extradite this murderer to be tried on Taiwan.
Different parts of China have different laws, because it's a big country with autonomous regions. Hong Kong, not that big, but for historical reasons have their own laws as well. If someone has an arrest warrant issued by one of the other Chinese governments, they will extradite the person to their jurisdiction. If it's a different country, with which China has an extradition treaty, then they will extradite them to Beijing (the Chinese national government) and Beijing will send them to that other country.
Taiwan is neither a separate country, nor a Chinese government whose arrest warrants Hong Kong respects. But the guy confessed to murder. He should be tried. So new legislation is required to make it legal to extradite him to Taiwan, either directly or through Beijing.
That was the initial controversy.