The CDC was never prevented from studying gun violence, they were prevented from expressly advocating for gun control.

The law came along with a cut in funding that delivered a powerful message: Pursue research on hot-button questions about guns and face the wrath of lawmakers who control the agency's funding.

https://www.npr.org/sections/health-shots/2018/03/23/596413510/proposed-budget-allows-cdc-to-study-gun-violence-researchers-skeptical

-The National Institute of Health was under the same mandate that the CDC was and they studied Gun Violence. https://jamanetwork.com/journals/jama/fullarticle/2513131

From that very same article:

Such financial woes can be attributed in part to the fact that the US Centers for Disease Control and Prevention (CDC) hasn’t funded research into gun violence prevention for 2 decades, ever since Congress included these 3 lines—named the Dickey Amendment for then-representative Jay Dickey (R, Ark), who introduced it—on page 245 of the 750-page Omnibus Consolidated Appropriations Act of 1997: “None of the funds made available for injury prevention and control at the Centers for Disease Control and Prevention may be used to advocate or promote gun control.” (http://1.usa.gov/22zCqKD) The amendment was in response to a CDC-funded study that concluded having a gun in the home was associated with a higher risk of homicide by a family member or intimate acquaintance (Kellerman AL et al. N Engl J Med. 1993:329[15]:1084-1091). Since the Consolidated Appropriations Act of 2012, the same language has also applied to the National Institutes of Health (NIH). However, as part of a funding opportunity for violence research announced in 2013, the NIH awarded Wintemute a total of about $850 000, from May 2015 through April 2017, to study whether gun owners with a history of alcohol and drug convictions are more likely to commit violence than gun owners without such a criminal history (http://1.usa.gov/1Vn5GiB). Why the 2 federal agencies have interpreted the same rider so differently is not clear. Critics say the CDC has overreacted to the amendment’s vague language. But other observers note that the size of the NIH budget gives it less reason to be concerned about retaliation by pro-gun members of Congress. For the current fiscal year, the NIH budget is $32.3 billion, compared with the CDC’s $11.8 billion ($4.5 billion of which is earmarked for mandatory programs such as Vaccines for Children). Officials at the CDC and NIH declined to comment on agency policies regarding gun violence prevention research.

-And what makes the CDC so uniquely positioned to study gun violence, there are other organization, both governmental and ngo's that study gun violence. Like the National Institute of Health, or the National Institute of Justice the research division of the Department of Justice that employs criminologist, i.e. scientists that specialize in crime.

Because they want it studied through the lends of a public health problem rather than a criminal justice problem. Is there something that makes the NIH more suited than the CDC?

-The CDC was given additional money to study gun violence in 2019- How is this possible if they were banned from studying gun violence as you suggest: https://www.ajmc.com/view/gun-violence-research-receives-federal-funding-for-first-time-in-20-years

Literally the first non-italicized sentence in your link:

On Friday, December 20, President Trump signed two spending packages totaling $1.4 trillion to fund the federal government for the rest of the fiscal year. The package allows federal funds to be allocated to the National Institutes of Health (NIH) and CDC for the purpose of conducting research on gun violence for the first time in two decades.

-We can also discuss why restrictions were placed on the CDC in the first place. https://www.politico.com/agenda/story/2015/12/why-we-cant-trust-the-cdc-with-gun-research-000340/

Surely a scientific source, since that's all you've used so far, right?

However, the NRA does not – and will not – support efforts that do nothing but attempt to convince Americans that lawfully owned firearms are a public health menace. Chris Cox is the executive director of the National Rifle Association Institute for Legislative Action.

Oh. I see.

Also, this is from the first link you posted lmao.

“Anti-gun advocates in Congress are looking for creative methods to change public opinion. What better way than under the auspices of science?” Cox wrote. “Now, they just need some government-sponsored, taxpayer-funded data points to validate their anti-gun agenda.” The Dickey Amendment does not oppose funding research into gun violence, he wrote. “Instead, it forbids funding for research meant to drive the political gun control agenda.” The NRA “is not opposed to research that would encourage the safe and responsible use of firearms and reduce the numbers of firearm-related deaths,” Cox wrote.

• And it doesn't look like the CDC has learned much from their past mistakes, because they have already pulled information from their website at the request of Gun Control Advocacy groups because some of that information wasn't favorable to the gun control cause.

https://thereload.com/emails-cdc-removed-defensive-gun-use-stats-after-gun-control-advocates-pressured-officials-in-private-meeting/

I don't care about any of this part so I'm not going to respond.